UC-NRLF 


SB    EST    Sfl3 


REESE   LIBRARY 

OF   THK 

UNIVERSITY  OF  CALIFORNIA. 

Deceived        MAS  33.1.894          \,89    . 
^Accessions  No.*  ^//2~ 


"NATIONAL." 

Patent  Taper  Protecting  Sleeve- Couplings. 
Iron  Fittings.  Brass  Goods. 

Ludlow  Gate  Valves  for  Gasf  Stea  in  or  Water. 
Ludlow's  Improved  Rubber- Faced  Fire  Hydrants. 

Steam  and  Gas  Fitters'  Supplies  and  Tools. 

All  Genuine  National  Tube  Works  Co.s'  Casing^ 

and  Tubing 
Is  fitted  with   perfect   V  Threads  and  Patent 

Taper  Sleeve  Couplings 
as  shown  in  above  cut.     They  are  shipped  with 

THREAD  PROTECTORS 
insuring  customers  perfect  goods  when  received 


Our  Casing,  Tubing  and  Drive  Pipe 

have  the  Best  Material  and  Workmanship,  and  are  acknowledged  to  be 

THE  STANDARD 

Our  works  are  the  largest  in  the  world  in  our  line,  and  the  only 
one  where  pipes  and  tubes  from  I  to  24  inches  inclusive,  are  manufac- 
tured. 


NATIONAL  TUBE  WORKS  GO,, 


Manufacturers  of 


Special  Lap-Welded  Pipe 

Fitted  with 

Converse  Patent  Lock  Joint. 


TRADE    MARK. 

This  special  pipe  is  well  adapted  for  the  conveyance  of  water,  gas 
or  air,  under  either  light  or  heavy  pressure;  is  tested  and  guaranteed 
to  stand  300  pounds-  per  square  inch,  and  is  thoroughly  protected 
against  corrosion  or  the  action  of  any  acids  or  alkalies  found  in  na- 
ture. 

It  can  be  bent  or  roughly  handled  without  cracks  or  injury  and 
can  be  laid  more  RAPIDLY  'AND  CHEAPLY  than  any  other  style 
of  pipe;  a  great  saving  in  FREIGHT  being  effected  on  account  of  its 
LIGHT  WEIGHT.  The  great  saving  in  FRICTION  in  this  pipe  enables 
SMALLER  sizes  to  be  used  and  equal  results  obtained,  and  a  conse- 
quent saving  in  first  cost. 

dL.  The  lengths  average  about  18  to  20  feet  and  require  about  one-half  the 
quantity  of  lead  per  joint  that  cast  iron  does.  The  joint  with  the  pipe 
has  successfully  stood  an  hydraulic  pressure  of  over  1000  pounds  per  square 
inch  in  tests  that  have  been  made.  Kalamein  alloy  imparts  nothing  inju- 
rious to  water,  and  Kalamein  pipe  may  be  safely  used  to  convey  drinking 
water  without  any  fear  of  contamination.  This  pipe  recommends  itself, 
through  its  many  desirable  features,  to  the  consideration  of  all  who  con- 
template using  pipe  for  water  or  gas  w°rks.  Information  and  prices 
promptly  furnished.  A  complete  line  of  Fittings,  Valves,  Hydrants,  Tools 
"tc..  etc..  are  manufactured  by  us  in  connection  with  this  pipe.  This  pipe 
lit!  over  4(tO  cities  and  villages  in  the  United  States ;  nearly  2000 
•  s  having  been  laid  in  the  pant  eight  years. 


W.  P.  BUTLER, 

GI1/IL  i  IRRIGflTION  ENGINEER, 


Irrigation 

Water  &  Sswags  plants 


AND 


DESIGNED    AND  SUPERINTENDED. 


Platting V 


Reservoirs  £^aid  Oaf. 
X^itehss  &  prains 
flames  Designed  &  J^aid  Oaf 
Estimates  /Aade. 


and 

or   Decorative. 


Roads  Laid  Oat,  Farm  Lines  Run  and  Corners  Relocated. 

COPIES  OF  THIS  BOOK   FOR   SALE,  25  CENTS. 
W,  P,  BUTLER,    ABERDEEN,  SOUTH  DAKOTA. 


IRRIGATION  MANUAL, 


CONTAINING 


Hgsful  Information  and  (Cables 


APPERTAINING    TO 
I*    « 


IN    THE    STATES    OF 


and  South  Bakota, 


TOGETHER    WITH 


Many  Tables,  Rules,  and  Items  of  Miscellaneous  Information, 


OF    VALUE    TO 


Farmer?  and  Bu?ine?s 


BY  W.  P.  BUTLER, 

Civil  and  Irrigation  Engineer,  Aberdeen,  S  D. 
1892. 


Let  tldny*  that  llamm  ve  abfyfyl'teSrned  by  doing  them.1 


HUKOX1TE    PRINTING 
HURON,   S.    D. 


Entered)  according  to  Act  of  Congress ,  in  the  year  1892,  by 

W.  P.  BUTLER, 
in  the  office  of  the  Librarian  of  Congress^  at  Washington. 


PUBLISHERS'  CERTIFICATE. 

HURON,   S.  D.,  June  ist,   1892 

The  publishers  of  this  book  hereby  certify  that,  in  accordance 
with  the  orders  of  the  author,  they  have  printed  and  bound  3500 
copies  of  the  same. 

SHANNON  &  LONGSTAFF, 

Publishers. 


INDEX  TO 


TABLE  SUBJECT.  PAGES 

NO. 

1  Dimensions  of  Standard  wrought  iron  pipe 16 

2  Prices  "        "     17 

3  Comparative  prices  of  different  pipes 18 

4  Prices  and  sizes  of  x  and  xx  strong  pipes 19 

"    casing  pipe 20 

6  Comparative  weights  of  different  pipes 21 

7  Dimensions  of  pipe  couplings 22 

and  weights  of  Kalamein  pipe 22 

9    Relative  area*  of  standard  pipe. 23 

10  Weights  and  sizes  of  cast  iron  pipe 23 

11  sizes  and  prices  of  spiral  riveted  pipe 24 

12  American  and  Birmingham  wire  gauges 25 

13  List  of  Dakota  artesian  wells 39 

14  Precipitation  during  irrigating  season  in  Dakota 44 

15  Water  duty  in  Colorado 46  ) 

16  '      "        ''      "    Dakota 48 

17  Weir  measurement  table k 56 

18  Table  of  Miner's  inches  reduced  to  cu.  ft.  and  gallons 58 

19  4k       "       "       inch  measurements 59 

20  "        *;    Second  feet  reduced  to  gallons 60  ^" 

21  Volume  and  Weight  of  water  on  one  acre 61 

2'1    Weight  of  water  in  pipes 62 

23  a        "        "      63, 

24  Pressureof     " 64*"' 

25  Volume  and  Wcght  of  water  in  9oo  feet  of  pipe 65 

26  Diameters,  areas,  and  contents  of  pipes  in  cu.  ft.  and  gallons.. ..        66 

27  Relative  discharging  capacities  of  pipes 67 

28  Friction  loss  in  j-ipes.  velocity  to  7  feet 68 

29  "  "          "20    "     71 

30  Tabular  numbers  for  computation  of  flow  of  water  in  pipes 72 

31  Horizontal  and  vertical  distances  reached  by  jets 63 

32  Table  for  calculating  the  horse  power  of  water 80 

33  Volume  per  minute  =  to  a  given  flow  per  day,  and  ) 

Volume  per  day  =  to  a  given  flow  per  minute ) 83 

34  Time  required  to  flood  different  areas  to  different  depths 84  f 

35  Volumes  thrown  in  different  times  by  wells  of  different  volumes 

per  minute 86 

36  Cubic  feet  reduced  to  gallons  and  gallons  to  cubic  feet 87 

'•M    V < >lumes  from  differen t  >\/.»<l  wells  in  1  and  3  months 88 

38  Discharge  of  jets  in  ga)l<  >ns  per  minute .' 89 

39  Size  and  capacity  of  wind  mills 90 

40  Volume  pumped  per  miuiite  by  wind  mills 90 

41  Velocity  and  force  of  wind 90 

42  Wind  in  Dakota,  for  past  9  years 91 

43  Rain    •'        "  "      "    10      "    91 

44  ( 1ross  sections  of  reservoir  banks 101 

45  Reservoirs,  areas,  diameters,  and  circumferences . .  102 

,  loss  by  evaporation  and  filtration 103 

,  areas,  diameters,  circumf's  and  contents  of  banks....  104 

,       ''    ,  and  volumes  at  different  depths 105 

49  "         ,  cost 106 

50  ',         ,  flow  of  water  from 107 

51  Depths,  sl<>],<-,  areas,  perimeters.  &c.  of  ditches 113 

52  Grades  per  jnile  and  per  KX)  feet 116 

53  Irrigation  statistics— -from  census  reports 137  * 


B 
Index  to  Tables^Continued. 

NUNBER.  SUBJECT.                                                                 PAGES. 

54  Table  of  time 154 

55  '    wages — 3  tables ...          155 

56  Sizes  of  a  one  acre  field 156 

57  Square  feet  in  different  areas 156 

58  Hills  on  one  acre 157 

58%    Measurement  of  angles  by  a  2  ft.  rule 158 

59  Tables  of  nails  and  spikes 160 

60  "        •'    wrought    "      160 

61  "        "    Manilla  rope 160 

62  "        "    well  digging , 161 

63  Capacity  of  cisterns  for  each  10  inches  of  depth 161 

64  "          "        "        in  wine  barrels 161 

65  Lumber  table— joist 163 

66  "      boards 163 

67  Decimals  of  a  foot  for  each  1-32  inch 164 

68  ."  "    an  inch  for  each  1-64  inch 165 

69  Square  roots  of  5th  powers  of  numbers 166 

70  lengths  of  circular  arcs 167 

71  Table  of  circles,  areas  and  circmuf's,  diameters  in  eights 169-171 

72  "        "        "  "        "           '•                                "    tenths....  172-171 

73  "        "        "  •'       "           "                  "           "twelfths..    178-184 

74  Table  of  sq.  and  cu.  roots  1  to  28,  advancing  by  tenths 185 

75  "        "    "      "      "      "    1  to  1000 186-193 

76  •'        •'    •'      "      "      "    1000  to  10.000 194-197 

77  '•        •!    Logarithms 198-200 

78  "        "    Tangents  and  cotangents 148-149 


INDEX  TO  FIGURES. 


FIG. 

1 
2 

Section  of  lap-weld  and  butt-weld  pipe  
"    pipe  couplings  

14 

20 

3 

Specials  and  pipe  fittings  

21 

4 

Section  of  a  "telescope"  well  

27 

5 

Perforated  pipe  in  well  

28 

6 

Spill-box  

-52 

7 

Illustrating  contraction  on  weirs  

5;-i 

8 

Weir,  and  method  of  water  measurement  

54 

9 

Miners  inch  measurement  

58 

10 

44                 44                                        4. 

59 

11 

Method  of  measuring  the  height  of  a  stream  

93 

12 

13 

Rainfall  and  temperature  map  of  Dakota  

94 

14 
15 

Slope  diagram  for  reservoir  banks  
Section  of  reservoir  and  bank  

98 
105 

16 

Form  of  gate  in  reservoir  bank  

108 

17 

Section  of  ditches  »  

Ill 

18 

"    ditch  

112 

19 

Pulsometer  pump  view  

127 

W 

4;                                    44                   <4 

128 

21 

Simple  form  of  level  

130 

?,2 

Leveling  rods  

131 

23 

Scales  —  decimal  and  duodecimal  

135 

24 

Measurements  between  inaccessible  points  

147 

GENERAL  INDEX. 


Aberdeen  well  .............. 

"        sewer  plant  ..............  7>> 

Acre,  size  of  circular—  ...........  157 

•4    foot  ..........................  60 

"     defined  ..............  51  61 

"    Hills  on  an-  ...............  157 

*A    Size  of  one—  ................  1  56 

Acreage,  to  compute  ........  156  157 

Angle.  Complement  and   supple- 

ment of  an—  ...................  152 

Angles.    Measurement   of    by   a 

2  ft.  rule  ........................  15S 

Apparent  level  ...................  135 

Apples  in  bin  .....................  162 

Area  of  farms  .............  45  139  144 

••      ••   fields  ................  156  157 

"    Relative—  of  pipes  ....  .......  23 

Arizona.  Irrigation  statistics  of.  137 
Artesian  wells  elewhere  ..........  37 

"     in  Dakota  .......  3s  41 

B 
Barrel.    Contents  of  a—  .........  162 

"     Weight  of  a  —  of  water  .....  63 

Board  measure  tables  ...........  163 

Brick  ............................  162 

Butt  welded  pipe  .................  14 

C 

Casing  pipe.  Prices  and  Sizes  of.  20 
Cast  iron  pipe.    Sizes  and  weights 
of—  .............................  23 

Center  of  pressure  .  ,  ..............  42 

Characters  .  Explanation  of—  ...  203 
Chimneys  ......................  162 

Circles.    Elements  of—  ......  152  153 

"        Explanation  of  tables  of  .168 
"      Tables  of—  diam's  in  Sths, 
.............  .  ......  169  to  171 

"       Tables  of  —  diam's  in  lOths 
..................  ..  172  to  177 

"       Tables  of  —  diam's  in  12ths 
..  ........................  178  to  184 

Circular  arcs.    Table  of-  ......  167 

Cisterns.     Capacity  of  —  for  each 

10  inches  ...............  161 

''       Capacity     of  —  in    wine 
barrels  .........................  161 

Conclusion  .......................  204 

Contents  of  pipes  .................  66 

Corn  and  hogs  ...................  154 

*'    in  bin  ........................  162 

Cost  of  ditching  .................  117 

<;      -  wells.r.  .................  34  36 

Couplings.    Kinds  of  —  ...........  18 

'•       Tablesof     ..............  22 

Cubic  ft.  on  one  acre  ..............  61 

'    •'  different  areas  .......  84 

"  in  pipes  ..................  66 

"   '*  reservoir  .............  105 

"  per  sec.  reduced  to  gals..  60 
''  reduced  to  Miners  inches.  59 


"        •'  gallons  ........  87 

"  thrown  in  1  and  3  months.88 
foot  is  equal  to  .............  151 

Cubes,  squares  and  roots  ____  lv:>  197 


Dakota  wells :;>•> 

"     Table  of— 39 

Datum  plane 129 

Day.   Astronomical — 154 

••     Siderial— 154 

•'     Mean  Solar— 154 

Decimals  of  a  foot  for  each  1-32 

inch 164 

"  an  inch  for  each  1-61.165 
Diameter.     To  find -to  discharge 

given  volume I'l 

Digging  wells 160 

Discharge  from  pipes 69  70 

To  find  volume   of    of 

pipes 72 

Discharging  power  of  pipes.    Rel- 
ative—... 67 

Ditches 110  to  120 

Area  of  section 112  113 

"    Contents  of  excavations  of  .119 
Ditching  machines  for — .. 

Ill  117  US 

Embankments     and    foot- 
ing of  - UN 

"      Excavation  and  cost  of.  117 

44      Flow  of  water  in  — 113 

"       Form  and  size  of— 110 

"      Gates  in— 119 

"      Grades  of— 1 15  116 

Location  of- 120 

*'      Laying  out — 117 

Length   of  wet   perimeter 

of— 112 

"      Maximum      velocity       of 

water  in— 114 

"      Mean    velocity  of    water 

in— 114 

Small  lateral— Ill 

"      Slopes  of — 113 

"      Table  of  areas  of  — 113 

"      "  grades  of — 116 

44      Widths  of— Ill 

Division     and    measurement   of 

water 49 

Divisors  for  water 51 

Drilling.    Suggestions  as  to— 33 

Drive  pipe 15 

Duty  of  water 43  to  4;* 

"      '*        "'     in  Colorado 46 

"      "        •'    Dakota 47 

"      '"        "  "         table 48 


Embankments  and  footings. . .   .11s* 

Entry  head 69 

Excavation.    Cost  of — 117 

Excavations.    Contents  of—  — 119 

Extra  and  xx  strong  pipes 15 

Evaporation  and  filtration 103 


Farmer.    The— 8 

Farms.    Size  of— 45  137  1 42 

Feet.    Cubic— see  cubic  feet 

"    Second — reduced  to  gallons. 60 


D 
General  Index— Continued. 


Fields.    Area  of— 156  157 

"    Laying  out— 120 

Filtration  from  reservoirs 103 

Flow  of  wells  per  day  and  per 

minute 83 

Flumes 120  to  122 

Formula  for  weir  measurements.. 57 

Foot.   Acre— denned 51 

Cubic — see  cubic  feet 

Decimals  of  a — 164 

4 '      Second— denned 60  51 

Footings  for  banks 118 

Francis'  formula  for  weirs 57 

Friction  head  defined 67  70 

"        loss  in  pipes 68  to  72 

Frosts  in  Dakota 92 


Gage  groupe  of  wells  in  Cal..  3S  i:{6 
Gallons=to  ......................  151 

in  pipes  ..................  66 

•'  reservoirs  ..........  105 

on  different  areas  .......  84 

"  one  acre.  .  .   ...........  61 

per  minute  defined  ......  51 

"  day  =  to  given  gallons 
per  minute  ____  ......  83 

"     per  minute  —  to  given  gal- 
lons per  day  ..............  83 

reduced  to  cubic   feet  ____  87 

"        <;  second  "     ----  60 

thrown  in   different    per- 
iods of   time  by  wells  of 
different  volumes  per  min- 
ute .....................  ...86 

'  •      thrown  in  1  and  3  months  .  .88 
"    by  jets  .........  89 

Gates  ...............  .....  41  107  119 

Gauges.    Water  —  ...............  65 

Wire—  .................  25 

Grades  of  ditches  ............  115  116 

"    Table  of—  ................  116 

Grain  in  bin  ......................  162 


162 
69 
69 
69 
69 


Hay 

Head  defined 

44     Entry— 

'    Friction — 

"    Velocity— 

'•    To  find— 72 

Height    of    a  stream.    To   meas- 
ure—  93 

Hills  on  an  acre 1 57 

Hitchcock  mill 81 

Hogs  and  corn .    154 

Horse  power  defind 82 

Horse  power  of  water.     To  find 

the— 80    | 

Hydrants 29    j 

Hydraulic  mean  depth 112    ! 

"        radius 112    I 

ram     124    | 

Idaho.    Irrigation  statistics  of — 137    < 
Illustrations,  see  index  to  Figures 
page  R . .    I 


Inch,  Decimals  of  an— for  each 

1-64 165 

Miner's— 51  58  59 

•'    in  California 59  60 

"    "  Colorado 59  60 

'    measurements 59 

"    reduced  to  gallons  and 

cubic  feet 58 

"     Statute— defined 51 

Irrigation.    Early  history  of — .6  76 

in  Dakota 7 

statistics  from   census 
reports .137 

J 

Jets.    Discharge  in  gallons  from .  89 

"    Distances  reached  by— 73 

•'    To  find  altitude  reached  by— 73 
•'     "    "    discharge  of— 73 

K 

Kalameinpipe 23 


Lap-welded  pipe 14 

Land.    Value  of— 137139141 

Lath 162 

Level.    The-- 129 

"    measurements. 135 

"    rod 131 

'    Simple  form  of — 130 

"    True  and  apparent— 135 

Leveling  explained 132 

"        for  a  reservoir 133  134 

"        Form  of— note  book  — 132 

Location  of  ditches 120 

"well 31 

Log  of  well 31  32 

Logarithms.    Explanation  as  to 

table  of- 201 

"  Table  of— 199200 

Use  of- 202 

"     "  tables  of— .  ..201 

Longitude,  length  of  degree 164 

Lumber 162 

"      tables 163 

M 

Machines.    Cable— 12 

Ditching— ....111  117  118 

Hydraulic- 13 

Jetting- 13 

Kinds  of- 11 

"        Pole- 11 

Mean  depth 112 

"    radius 112 

Measure.    To— the    height  of    a 

stream 93 

Measurement  of  angles  by  a  rule.158 

"        and    division  of  water  49 

of  water  by  a  weir.  .53 

Units  of— of  water ...  51 

Measures  and  weights 150  to  153 

Melville  law, 8  31 

Mensuration 150  to  153 

Mill  sites  79 

Mills  at  Hitchcock 77   78  81 


E 


General  Index — Continued. 


Mill*  at  Springfield M 

"  Woonsocket 7S  si 

41        "  Yankton sl 

11    mnbywella  77  TS  si 

Miner's  inch 31  :>s 

"inCal.  andCol 5960 

''   reduced   to  gals  and 

cuft 58 

Miner's  inch  measurements 59 

Miscellaneous  information 162 

Module  defined 31 

Montana.     Irrig'n  statistics  of— 137 

Mortar        162 

Multipliers.     Useful     153 

N 

Nails.  Tables  of— and  spikes..  .160 
Nettleton.  Letter  from  Col.  E.  S..75 
Nevada.  Irrigation  statistics  of.  137 

New  era  grader  and  ditcher 117 

New  Mexico.  Irrigation  statistics 
of- 137 


Outlets  and  gates 41  107 


Perforated  pipe 2s 

Perimeter.     Wet— 112  113 

Photographs  of  wells 143  146 

Description  for — ..  .144 
List    of  —  and  pho- 
tographers  146 

Photographs.     Where  to  buy—. .  146 

Pipe 14  to  28 

'    Butt  welded— 14 

'    Casing — .  prices  and  sizes. .  .20 

"    Cast-iron— 23 

"    Contents  of— 66 

"    Drive— 15 

''    Friction  loss  in — »>-S  to  72 

1     Kalamein— 22 

Lap-welded— 1415 

'    lines.     Advantage  of — 123 

'•    for  distribution...  122  123 

Perforated—         28 

Prices.     Comparative— of— .IS 

Prices  of  standard — 17 

Relative  areas  of — 23 

u  discharging  powers  of — 67 

Spiral  riveted         24 

welded- 27 

Standard- 16 

Vertical  opening  to— 30 

'    weight  of — Comparative — ..21 

'    Weight  of  water  in— 62 

'    x  and  xx — 15 

'•       Prices  and  sizes  of— 19 

Polygons 153 

Power.    Horse— 82 

of  wells 77  to  82,204 

'    To  calcula  te  horse—  80 

Precipitation.    Distribution  of— 44 

in  Colorado 44 

"  Dakota 91,92 

•'          "         in  April 
and  May 44 


Precipitation  map  of  Dakota 94 

Pressure  and  volume.    Relation 

between 9 

in  900  feet  of  pipe 65 

"        of  wa ter,  table 64 

Static— 9 

To  find— of  water 64 

Prismoiclal  formula 157 

Pumps 125tol28 

"    Cost  and  duty  of—. . .  .125  126 
"    Pulsometer— 126  to  128 


Rain  making 26 

"     in  Colorado 44 

"      "    Dakota 4491  92 

Ram.    Hydraulic— 124 

Reaming 14 

Relative  areas  of  pipes 23 

"        discharging  capacity  of 

pipes 67 

Relative  weight  of  pipes 21 

-Reservoirs .96  to  10$ 

44       Areas,  Diams,   Circumfs 

of- 102 

"       Areas,  Diam's,  Circumfs 
and  cubic    capacity   of 

banks  of— t.t 104 

44        areas   and  capacities  at 

different  depths 105 

"       Banks  of— - 

99  100  101  104  117  119 

44  "          Diagrams  of — 100 

Sections  of— ..101 

Washing  of— ..100 

44        Capacity  of— at  different 

depths 105 

"  Circumferences  of — ... 

102  to  105 

Cost  of— 106  117 

"  grading  of  banks  of  117 
Diameter?  of— .102  to  105 
Evaporation  from — . .  103 
Filtration  "  ....103 
Flow  -  ....107 

"  Form  of— 97 

Footings  for  bank  of— 119 
Laying  out—  ...9*  133  134 

Location  of— 97 

Outlets  and  gates  from 

41  107  108 

Sections  of  banks  of — 101 

41  Size  of—..  .97  102  104  105 

"     '•  To  calculate  -.10:5 

Slopes  of  banks  of—.  .100 

"    Sub— and  storage  ditches. 10S 

'•    Washing  of  banks  of — . . .  100 

Rod.    Leveling— 131 

Rope.    Manilla— 160 

Roots.    Explanation  as  to  tables 

of- 198 

44      Sq  &  cube— 1  to  28  by  lOths  185 

"  "      '•    1  to  1000..  186  to  193 

••'.'•      4i  1000  to  10000.194  to  197 

I       "  To  figure— by  logarithms.200  202 


F 

General  Index  -Continued. 


Scales,  decimal  and  dnodecimal.135 
Second  foot  ...............  51.00 

11    reduced  to  gallons..  .60 

Sewer  plant  at  Aberdeen..  .        .     7^ 

Shingles  .........................  102 

Size  of  farms,  .................  137.1-12 

'     "     pipe,  see  Pipe  ............  .. 

"     ik    reservoirs,  see  Reservoirs  .  . 
Source  and  sni)j)ly  of  water  .....  74 

Specials  ..........  '  ..............  29.  30 

Illustrations  of—  .         ...21 

Setting  of—  99  30 

Spikes  and  nails  ...   '.  '.  V  160 

Spillbox  ........................  r,2 

Spiral  riveted  ])ipe  ........  24 

"    welded    *'  27 

sprmgfieid  mill.  ..:::::::::::::::.  si 

Square  and  cube  roots  ....  185  to  197 

"    roots  of  5th  powers  ....  61  166 

Squares  ...................  150  to  1"2 

and  cubes  .......  185  to  193 

Static  pressure  ................  9,  bo 

Statistics  of  irrig'n  in  7  states.:  137 
Statute  inch  .....................  ol 

Stonewall...  ....................  C2 

Storage  ditches  .................  108 

Stream.  To  measure  height  of  a-93 
mbject,    Ihe-  ..................     6 

Sub-rervoirs  ...................  ..108 

hu  b~surtace  waters  ..............  125 

Suggestions  as  to  drilling  ........  33 

Supply  of  water  ..................  74 

T 

Tables  -See  index  to  tables  page  A 
Tangents  and  cotangents.  .147  to  149 
Telescope  weU.  .  .  .27 

Temperature  in  Dakota  .......  i  2  94 

Theoretical  velocity  of  water  ____  70 

Threads  of  pipe  ..............  18 

Time     Table  of—  154 

"     'required  for  'different  ."sized' 
welfs  to  tlm.w  given  volumes 
of  water  ......  .....  S4 

-  Volumes  thrown  in  differ- 
enf  periods  of—  by  wells  of  given 
volumes  per  minute.  S(> 

Ton.   Weight  of  one-of  water...  .03 

Tools.  14 

Triangles'.'.'.''.'.'.'.   '.'  .'.'.'i"2 

True  and  apparent  level  ........  135 

U 

Units  of  water  measurement  .....  51 
Useful  multipliers  ....  .  153 

Utah.    Irrigation  statistics  of—  137 


Value  of  land  ...........  139  to  141 

"water  .............  136  to  139 

Valves  ............................  29 

V  egeta  tion  and  wa  ter  ...........  76 

Velocity  head  ...................  09 

Maximum      surface—  in 
streams  ................  114 


Velocity  Menu     of  streams  .......  Hi 

of  sound  in  air  ...........  90 

-water  .......  90 

rjieoretical—  ...........  70 

of  wind.  .        .  ............  90 

''  m  Dakota  .......  91 

.       '•'          «  ^S8'    To  get  the~   '  '  82 
V  olume  of  wells.......   ...  50 

))('r  (rtay  *  Per.mm  °? 
"  !n  ]  &?  months.  ..88 
-  '  in  diftprent  pen-  ^ 


.  ...... 

of  wells  m  different  per- 

iotls  of  time  ......... 


„  difterent  areas  ........  84 

Relation  between  —  and 

pressure.         .....  910 

To  compute—  discharged 
bv  P^08      ..............  72 

W 
Wages.    Table  of-  ......    .....  155 

Water  4°  to  76 

u    and  vegetation.'..'.''.'.'."..   ...76 

u    Annual  cost  of-  ............  138 

•<    ("enter  of  pressure  of-  ......  42 

*«     Densitv  of—  63 

«    Distribution  of  '  -.'  .'..'.  m  to'm 

M        by  ditches.  110  to  120 

«         "  flumes.  .123  to  122 

«  •  •         "pipes      1  '>2  to  1  23 

«  ••         •«  r.im  _  '  124 

-  .«         "  pumps"  &"  wind 

mills  .............  124  tol2S 

'    Division   and  measurement 

4     T°  7'  '  V  ...............  '«V;  '  i« 

<    Duty  of-.  .  .  .  43  to  48 

..      '',  ~™  k°11orflcl°-  '^'3 

.,  -Refereences  to-4o 

Evaporation  of—  .........  103 

glo^.of~T  t?itc1^'  •11lt?  ll* 

£riCt,101;  °f~m  P1P°S  '  '  M  tO  ^ 
Head  of-  .....   ..............  69 

4    Horse  power  of-  ...........  80 

,    Vi  r<?servoirs  ...     ......  ...  .  .  10t> 

Maximum  surface    velocity  ^ 

,    ^Velocity  of-V  '.  ^  .T.m 
Measurement  and  division 


"'     on  one  acre,  vol.  and  weiglit.61 
"  different  areas  .........  .84 

Phreatic—  ................  125 

'     Figure  of  -  ............  4264 

(enter  of—  .........  42 

4<        to  find-  ............  64 

'•    Properties  of-  .............  42 

•'     Seepage  of—  ................  46 

"     Source  and  supply  of—  ......  74 

"     Sub-surface—  ..............  1  25 

"     Units  of  measurement  of—  .  51 
"     Value  of—  ...........  186  to  139 

"     Velocity  of-  ...............  114 


General  Index  -Concluded. 


Water  Volume  of^-in  pipes.    ...     »'•'>    '    Wells  Location  of  -  ...............  31 

••  --on  1  acre  ........  lii  •'     Log  of—  ..................  3132 

on    dinVn-nt  "     Number  in  Dakota  ............  '.' 

arras       ..................  M  "     Photographs  of—  ...  145  to  148 

"     Weight  of-  ..................  W  Whore  to  buy—  14* 

'—in  pipes  ........  »i-J  •     Power  of  ..........  «.">  &  67  to  82 

'  —  on  an  acre  ......  <»1  k     Source  A:  supply  of  Wilted  of.  74 

u  bbl.,  gaL,  qt.,  pt,  •     Telescope  ..................  27 

ic  of"  .....................  63    :         '     used  for  mill  power  ____  77  to  Nl 

Weather  in  Dakota—  table  .......  £2  "    Velocity  of  How  of.  ..  ........  (M 

Weight  of  cuft  of  substances  —  159    ;  "          "    •'      ;'  To  got—.  .82 

different  pipes.  16  to  24    j        "    Volume  of—  not    dependent 

i-      water  ........     01  to  65  upon  sizo  ..................  V« 

Weights  and  measures.  .  .  .  150  to  1T),3  '     Volume  of     per  day  and   per 

Weir  ............................  51  minute  .....................  s:  ; 

'     Application  of-  table.  ..          55  '*     Volume  of  —  in  1  <fc  3  mos  .....  Sb 

44     Conditions  of  operation  of  a—  Wet  perimeter  .............  112  11  3 

.........................  52  53  Wind  in  Dakota  ..................  91 

'    Formula  for  —  measurements  57  "    mills     ................  27  90  1  26 

•  Illustration  of  a—  .......  5854  "    Velocity  and  force  of—  ......  90 

'    table  ......................  5»i  Wire  gauges  .....................  25 

'    To  construct  a  —  ............  53  Woonepcket  mill  ..................  HI 

Weisbach's  formula  .............  70  Wyoming.  Irrig'n  statistics  of  -137 

Well.  Aberdeen-  .............  38  39 

"    digging  .....................  161 

Wells.    Cost  of—  ......  -  ........  :U  3<i 

14    Dakota-  .................  :W  41  AYZ 

il    Table  of—  ............  :«» 

'     Ecfuiomy  of  large  and  small  10  x  and  xx  pipe  .....................  1." 

•  elsewhere  ................  37  38  prices  and  sizes  of.  li« 

'     height    of     stream      of  —  To  Yankton  mill  ...................  81 

measure  .....................  93  Yard.    A  cubic—  is  equal  to—  ----  151 


INDEX  TO  ADVERTISEMENTS. 


Abendroth  <5c  Root  Mfg  ( 'o. .  23s  239 

Addyston  Pipe  <k  Stool  Co 216 

American  Well  Works 252 

Austin,  F.  ( '.  Manfg  Co 218  219 

B.elknap  Motor  Co 237 

Blair  Camera  Co 222 

Brass  &  Iron  Works  Co  . .    . .        225 

Buff  &  Bergor 215 

Butler,  W.  P 2 

ghapman  Valve  Co 210 
hicago  Water  Motor  Co 211 

Clow,  J.  B.  k  Son 806 

Crane,  G.  W.  &  Co 213 

Consolidated  Land   «Sc  Irrigation 

Co 251 

Dakota  Irrigation  Co 2*5 

Dennis  Long  &  Co 217 

Engineering  Magazine. 231 

News . 

First  National  Bank 250 

Gurley,  W.  &  L.  E 22  >  221 

Harper  &  Brothers 240 

Irrigation  Age 239 

Leffel,  James,  Co 229 

Ludlow  Valve  Manfg  ( 'o 224 

National  Tube  Works  Co.,  Front 


Cover  and 1 

Nye  Steam  Vacuum  Pump  Co... 247 

Oil  Wrell  Supply  Co 227 

Pech  Manfg.  Co 223 

Peltori  Water  Wheel  Co 2?6 

Pulsometor  Pump  Co 127  1*  244 

Railway—  Chicago  A:  North 

\Vestern  .  230  231 

Railway  —  Chicago,  Milwaukee 

k  St.  Paul 232  233 

Railway  -Great  Northern 235 

Northern  Pacific 286 

Reading  Iron  Co.  (Back  Cover) 

Rife's  Hydraulic  Engine  Co. .  214 

Robinson  &  Cary  Co 242 

S wa  n  Broth ors 243 

"  A-  Stacey  ( W .  E.  Swan  Co.)  .228 

Trautwine,  J.  C . .  215 

Valley  Land  Jt  Irrigation  Co 250 

Western  Wlieeled  Scraper  Co..  .246 

Williams  Brothers 207 

Well  Machine  A:  Tool  Co 212 

Young  A:  Son '.'40  '241 

See  Index  to  articles  advertised  on 
next  page. 


H 


INDEX  TO  ARTICLES   ADVERTISED. 


Banks* 

First  National,  Huron,  S.  D.   . .  .250 
Boilers. 

Oil  Well  Supply  Co 227 

Robinson  &  Cary  Co 242 

Books, 

This  book,  W.  P.  Butler 2  41 

Engineering,  J.  C.  Trautwine.  ..215 

Irrigation,  Irrigation  Age 209 

Harper's  Periodicals 249 

Cameras. 

Blair  Camera  Co . . .222 

Coffee  Mills  and  Dynamos. 

Belknap  Motor  Co 237 

Civil  Engineer. 

W.P.Butler 2 

Driller*. 

Swan  Brothers 243 

Swan  &  Stacy 228 


Electrical  Supplies. 

Belknap  Motor  Co  237 

Engineering  Publications. 

Engineering  Magazine 234 

News 208 

J.  C.  Trautwine 215 

Hydraulic  Rom. 

Rife's  Hydraulic  Engine  Co 214 

Hydrants. 

See  Valves 

Irrigation  ('oinp«nies. 
Consoldated   Land  «fc  Irrigation 

Co ." 251 

Dakota  Irrigation  Co 245 

Valley  Land  &  Irrigation  Co 250 

Levels. 

Buff  <fc  Berg.v .  .215 

W.  and  L.  E.  Gurley 220  221 

Young  &  Son 240  241 

Machines — Ditching  and   Grading. 

F.  C.  Austin  Manfg  Co 218  219 

Western  Wheeled  Scraper  Co.  ..246 

Machine*  -  U>//  /trilling. 

American  Well  Works 252 

Austin,  F.  C.,  Mfg.  Co 218  219 

Brass  &  Iron  Works  ( V> 225 

OH  Well  Supply  Co 227 

Pech  Manfg.  Co  228 

WTell  Machine  &  Tool  Co 212 

Williams  Brothers 207 

Machines— Roa  <  1 . 

F.  C.  Austin  Mfg.  Co 218  219 

Western  Wheeled  Scraper  Co.  ..246 


Motors— Electric  « »<1  \ \ '« ter. 

Belknap  Motor  Co 237 

Chicago  Water  Motor  Co ..211 

Jas.  LeffelCo 229 

Pel  ton  Water  Wheel  Co 226 

Pipe— Cast  Jron. 
Addyston  Pipe  &  Steel  Co. ..... .216 

Dennis  Long  &  Co 217 

Robinson  &  Cary  Co 242 

Pipe —  Wrought  Iron. 

American  Well  Works 252 

J.  B.  Clow  &  Son 206 

G.  \V.  Crane  &  Co 213 

National  Tube  Works  Co.,  Front 

Cover  and 1 

Oil  Well  Supply  Co 227 

Reading  Iron  Co.,  Back  Cover 

Robinson  <fc  Cary  Co 242 

Pipe—Riveted. 

Abendrotli  &  Root 238  239 

Pumps. 

American  Well  Works *  ... .252 

Nye  Steam  Vacuum  Pump  Co. .  .247 

Oil  Well  Supply  Co 227 

Pulsometer  Pump  Co.  ..127  128  244 

Robinson  &  Cary 242 

Railways. 

Chicago  &  Northwestern 230  231 

Milwaukee  &  St.  P. 232  233 

Great  Northern 235 

Northern  Pacific 236 

Scrapers. 

F.  C.  Austin  Mfg.  Co 219 

Western  Wheeled  Scraper  Co. . .  .246 

Specials— for  Pipe. 

Addyston  Pipe  &  Steel  Co 216 

Dennis  Long  <fe  Co 217 

Robinson  &  Cary  Co 242 

Kfectin.  Goods. 

G.  W.  Crane  &  Co.... 213 

Vctfaes. 

American  Well  Works 252 

Brass  &  Iron  Works  Co 225 

Chapman  Valve  Co 210 

Ludlow  Valve  Mfg.  Co 224 

National  Tube  Works  Co.,  Front 

Cover  and 1 

Robinson  &  Cary  Co 242 

Wnfrr  ir//ro/x. 

See  Motors 

11  '<>}}  Mticln'neri/. 

See  Machines— well  drilling 

\\'im?  Mills. 
Pech  Manfg.  Co 223 


PREFACE. 

The  idea  in  presenting  this  little  book  to  the  public  is  to 
supply,  in  part,  a  demand  for  such  tabulated  and  general  in- 
formation as  is  needed  by  many,  at  the  present  time,  who 
are  becoming  interested  in  the  matter  of  irrigation.  Few 
have  access  to  books  of  tables  and  rules  and  fewer  still  are 
able,  without  them,  to  figure  out  the  problems  involved,  and 
bence,  many  abandon  the  subject  because  unable  to  culti- 
vate an  interest  sufficiently  satisfactory  to  themselves  to 
warrant  the  taking  of  some  definite  step  in  the  direction  of 
a  practical  trial  of  that  which,  if  properly  managed,  must 
open  up  the  road  to  fortune  to  all  who  choose  to  enter. 
The  idea  is  not  to  present  an  exhaustive  treatise  on  irriga- 
tion, or  to  treat  at  length  any  of  the  matters  presented,  but 
simply  to  suggest  them  and,  by  giving  many  rules  and  tables, 
to  supply  the  information  needed,  so  that  each  may,  for 
himself,  make  such  estimates  as  the  circumstances  of  his 
own  case  may  require;  and  further,  to  put  the  investigator 
in  the  way  of  obtaining  such  desired  information  as  cir- 
cumstances would  not  permit  of  being  given  here. 

In  the  selection  of  many  rules  and  tables  the  following 
standard  works  have  been  freely  consulted  and  properly 
credited : 

Haswell's  Engineer's  Pocket  Book,  (Harper  <fe  Bros.,  New  York.) 

Trautwine's  Engineer's  Pocket  Book,  (John  Wiley  <fc  Sons,  New  York.) 

Engineer's  Pocket  Book,  1876,  (Lockwopd  &  Co.,  London.) 

Uuseful  Information,  (Jones  &  Laughlin,  Pittsburgh.) 

The  Measurement  and  Division  of  Water,  (L.  G.  Carpenter,  Ft.  Collins, 

Colorado.) 

Pocket  Companion,  (Carnegie  Phipps  &  Co.,  Pittsburgh.) 
The  trade  cataloges  of  the  Chapman  Valve  Mfg.  Co.,  National  Tube 

Works,  James  Leffel  &  Co.,  Addyston  Pipe  Co.,  Pelton  Water  Wheel  Co., 

Reading  Iron  Co.,  and  others. 
State   and  government  reports,  and  all  other  available  and  reliable 

sources,  such  a?  the  Engineering  News,  Irrigation  Age,  and  Scientific 

American. 

Besides  the  matter  thus  compiled,  many  entirely  new 
tables  have  been  computed  to  answer  the  special  require- 
ments of  those  to  whom  this  matter  is  addressed. 

If  the  matter  presented  is  instrumental  in  creating  any 
new,  or  in  fostering  any  present  interest  in  irrigation,  or  in 
aiding  any  in  need  of  such  information  as  is  presented,  then 
will  the  object  of  the  compiler  have  been  accomplished. 

In  the  hope  that  hereby  a  demand  has  been  partially  sat- 
isfied this  little  book  is  inscribed  to  the  advocates  of  irriga- 
tion in  the  Dakotas,  by 

W.  P.  BUTLER, 

Compiler. 


THE  SUBJECT. 

Much  valuable  time  is  wasted  in  the  preparation  and 
printing  of  articles  on  irrigation  the  burden  of  which  seems 
to  be  to  remove  a  doubt  as  to  whether  irrigation  will  pay,  if 
practiced  in  the  Dakotas. 

The  chief  object  accomplished  by  such  articles  is  to  keep 
alive  the  very  doubt  they  aim  to  overcome,  and  at  a  time 
when,  and  in  a  place  where,  a  doubt  will  do  the  most  harm. 
The  only  good  accomplished  is  that  the  subject  is  kept  open 
and  before  the  public. 

THERE  IS  NO  DOUBT 

as  to  irrigation  paying  in  Dakota,  and  this  may  be  abund- 
antly shown  by  a  study  of  the  history  of  irrigation  in  this 
and  other  lands. 

Irrigation  is  as  old  as  the  race  and  it  has  been  both  the 
heritage  and  the  legacy  of  every  tribe  and  nation.  The 
dawn  of  history  dimly  reveals  the  practice  by  those  ancient 
peoples,  and  history,  both  sacred  and  profane,  has  recorded 
its  onward  march,  as  it  has  the  march  of  armies.  In  Pales- 
tine, in  Egypt,  in  Assyria  and  in  India  it  was,  as  it  still  is, 
the  life  of  the  people.  As  irrigation  developed,  empires 
arose,  and  with  its  fall  they  fell;  and  where  was  once  the 
verdant  homes  of  countless  millions  there  is,  to-day,  a  des- 
ert waste. 

The  legions  of  Home  may  be  said  to  have  been  supported 
by  irrigation;  for  the  Roman  Empire  was  but  a  union  of  ir- 
rigated nations.  The  subject  in  that  day  having  the  sanc- 
tion and  fostering  care  of  every  monarch.  As  the  world  has 
developed  so  has  irrigation— until  to-day,  a  large  percentage 
of  the  products  of  the  world  are  raised  by  that  means;  and 
now,  as  in  all  past  ages,  those  who  till  the  soil  under  a  sys- 
tem of  irrigation  are  the  most  prosperous  of  their  class,  and 
their  lands  the  most  valuable  of  air  devoted  to  purposes  of 
agriculture. 

Irrigation  has  developed  during  these  ages,  as  has  every- 
thing else;  now  progressing,  and  again  declining,  with  the 
progress  or  decline  of  the  arts  and  peoples  of  each  age  and 
nation.  The  system  of  Spain  was  not  that  of  Italy,  nor  is 
the  system  of  to-day  the  same  as  that  of  a  century  ago. 

The  literature  of  irrigation  is  most  interesting,  and  every 
irrigator  in  the  Dakotas  should  "read  up"  to  the  fullest  ex- 
tent. 

The  system  of  irrigation  practiced  in  every  country  has 
been  a  development,  not  alone  in  its  engineering  sense  but 
in  its  legal  sense  also;  for  the  questions  of  water  rights  and 
appropriations  have  always  been  most  intricate  and  have 
demanded  most  studied  treatment. 

Irrigation  in  the  United  States  was  first  practiced  in  the 
Salt  Lake  valley  and  in  lower  California,  although  very  ex- 
tensive systems  of  irrigation  works,  built  by  the  aborigines 


were  in  ruins  when  the  earliest  settler  went  into  the  country. 

The  ancient  inhabitants  of  Mexico  and  of  Peru  had  vast 
systems  of  canals,  aqueducts  and  tunnels  for  the  purpose  of 
water  supply  and  irrigation,  so  that  the  industry  of  the 
white  man  is  but  a  revival,  on  this  western  continent,  of  the 
older  irrigation  system  of  the  ancients. 

From  the  crude  beginnings  of  the  pioneers  who  lacked 
both  capital  and  labor,  and  were  forced  to  begin  anew,  with- 
out previous  knowledge  of  the  subject,  and  under  new  con- 
ditions, there  has  developed  in  our  western  states  a  system 
of  irrigation  so  vast  that  its  worth  is  measured  by  the  tens 
of  millions,  and  so  perfect  as  to  bear  most  favorable  com- 
parison with  the  older  and  highly  developed  systems  of 
Spain,  Italy  and  India.  Each  state  has  done  all  in  its  power 
to  foster  the  industry,  to  encourage  investment  in  plants 
and  securities,  and,  by  systems  of  law  best  suited  to  their 
special  conditions  and  requirements,  to  surround  the  indus- 
try with  all  needed  protection. 

IN    DAKOTA 

the  day  was,  when  to  have  spoken  of  irrigation  as  necessary 
to  our  wellfare,  would  have  been  to  have  uttered  heresy. 
That  day  has  passed.  The  bitter  experience  of  a  series  of 
dry  years— when  the  hot  wind  was  all  we  reaped— has  taught 
the  lesson  that,  to  live  in  prosperity  and  pleanty  in  Dakota, 
we  must  irrigate.  It  is  no  crime;  it  is  no  disgrace;  for  the 
most  fruitful  lands  on  the  earth  are  such  as  are  irrigated 
and  such  as  would  be  a  barren  waste  were  it  not  for  irriga- 
tion. Such  lands  are  in  the  deserts  of  Arabia,  Africa  and 
our  own  western  states.  No  better  soil  or  climate  exists  on 
this  continent  than  that  of  Dakota  and,  with  water  at  our 
bidding,  none  on  earth  will  be  more  f  ruitfull. 

No  country  in  the  world,  so  far  as  known,  possesses  what 
Dakota  does— a  soil  of  unmatched  fertility,  a  climate  suited 
alike  to  the  best  needs  of  plant  and  animal  life,  a  topography, 
or  surface,  best  suited  to  a  system  of  general  irrigation,  and 
at  the  minimum  of  cost,  and  a  supply  of  water  as  general 
in  its  distribution  as  it  is  inexhaustable  in  its  volume  and 
powerful  in  its  flow . 

What  a  combination  is  this  V  Soil— climate— topography 
— water  and  power.  Each  perfect;  each  in  accord  with  the 
other;  and  all  to  be  had  and  controlled  by  him  who  wills  it. 

A  Dakota  farmer  need  not  wait  for  a  rich  company  to 
build  a  dam  to  impound  the  clouds  and  then  beg  life  on 
such  terms  as  the  company  may  care  to  fix. 

He  has  but  to  prick  the  soil  and  a  fountain  of  wealth 
pours  forth  to  do  his  bidding.  A  servant  as  powerful  as  the 
elements,  yet  as  subject  to  control  as  the  child;  more  bur- 
dened with  wealth  than  the  summer  shower  and  less  bur- 
dened with  disaster  than  the  summer  torrent.  A  servant 
perfectly  trained  to  the  performance  not  alone  of  one  duty 
but  of  many,  and  a  servant  the  like  of  which  nature  has  not 
vouchsafed  to  the  service  of  the  men  of  any  other  land. 


8 

THE  FARMER. 

Has  he  had  abundant  crops  ?    No! 

Does  he  need,  and  must  he  have,  a  well?    Yes! 

HOW  WILL  HE  GET  IT  ? 

No  solution  is  offered  as  to  the  means,  but  it  is  giving 
good  advice  to  say— A  dopt  any  means.  Some  will  be  more 
advantageous  than  others  yet  to  most  farmers  it  will  not  be 
a  matter  of  choice. 

ANYTHING  TO  GET  A  WELL! 

The  "  Melville  "  law,  providing  for  township  wells,  has  not 
been  a  success  for,  although  115  wells  were  located  by  the 
State  Engineer  during  1891,  and  bonds  voted  for  them,  no 
market  (except  in  two  cases)  has  yet  been  found  for  these 
bonds  because  of  the  manifest  injustice  of  the  law,  which 
provides  for  the  assessment  of  property  not  in  the  least  ben- 
efited, or  needing  any  benefit,  in  order  that  other  private 
properties  may  be  developed.  Investors  look  askance  at  se- 
curties  having  so  strong  a  taint  of  unconstitutionality  and, 
as  a  result,  there  are  few  such  wells  being  drilled;  the  ac- 
tivity being  confined  almost  wholly  to  purely  private  enter- 
prises. 

A  more  equitable  law  must  be  passed  to  give  relief.  If 
the  present  law  can  be  made  to  work,  well  and  good,  take 
that  means.  If  a  mortgage  company,  or  an  individual, 
stands  ready,  under  any  one  of  an  infinite  number  of  plans, 
to  put  down  a  well  for  you,  take  it  at  once.  Raise  the  mon- 
ey in  any  way— only  raise  it! 

If  you  can't  own  a  whole  well,  own  part  of  one.  If  you 
can  own  it  all,  do  so  by  all  means,  for  joint  ownership  means 
joint  responsibility  and  its  attendent  evils. 

Part  of  a  well  is  better  than  no  well,  and  40  acres  "under 
water  "  is  better  than  640  acres  under  a  hot  wind.  Loose  no 
time  in  stopping  to  figure— as  many  are  continually  doing — 
whether  irrigation  will  pay  or  not,  for  it  never  did  anything 
else  but  pay,  here  or  elsewhere.  If  you  want  a  life  job  take 
that  of  trying  to  prove  that  irrigation  ever  failed  to  pay  and 
pay  well.  Let  the  first  task  be  to  get  the  money,  figure  on 
that  and  then  when  it  is  obtained  there  will  be  time  to  figure 
on  its  use. 

The  details  of  an  irrigation  plant  in  Dakota  are  very  sim- 
ple as  compared  with  those  in  most  other  sections,  where  the 
sourse  of  water  supply  is  at  a  great  distance  and  where 
heavy  dams,  long  and  expensive  flumes,  tunnels  arid  bridges 
must  be  built  either  to  store  or  to  convey  it.  These  great 
engineering  works  entail  a  vast  expense  and  preclude  any 
individual  ownership  or  controll.  Here,  however,  the  whole 
system  of  supply  and  distribution  may  be  created  upon,  and 
limited  to,  ones  own  garden  patch  and  at  but  nominal  cost. 

Where  other  systems  prevail  there  enters  in  the  very  com- 
plex questions  of  water  rights,  which,  to  a  great  extent,  can- 
not find  a  place  here  where  the  system  is  so  different  and 


essentially  individual.  If  a  farmer  owns  a  well  he  can  use 
it  when  and  as  he  chooses,  and  to  any  extent,  so  long  as  he 
does  not  trespass  upon  his  neighbor;  and  he  may  sell  the 
water  on  such  terms  as  he  may  be  able  to  make.  Nor  can 
he  prevent  his  neighbor  seeking  a  supply  from  the  same 
source,  for  whence  the  supply  comes  and  what  its  volume 
may  be  can  never  be  other  than  conjecture. 

That  questions  of  water  rights  as  between  individuals, 
and  as  between  the  State  and  individuals,  will  arise  there 
can  be  no  question,  but  what  questions  will  arise  and  what 
their  solutions  will  be,  may  be  safely  left  to  the  future. 

After  the  question  of  money  supply,  the  first  consideration 
is  as  to  the  well. 

THE  WELL. 

About  200  wells  have  already  been  put  down  in  the  two 
Dakotas,  varying  in  size  from  2  to  8  inches.  The  popular 
and  common  sizes  being  4J^  and  6  inch  wells.  On  the  whole, 
very  little  is  yet  known  of  our  wells  because  of  lack  "of  sys- 
tematic study  and  experiments.  Then,  too,  very  many  er- 
roneous ideas  prevail  as  to  the  wells  and,  unfortunately,  any 
amount  of  wilful  exageraation  which  will,  in  the  end,  result 
in  more  harm  than  good. 

A  few  facts  will  be  stated  and  explained. 

The  volume  of  a  well  does  not  depend  upon  its  size,  that 
is,  an  8  inch  well  will  not,  necessarily,  discharge  more  water 
than  a  6  inch  well.  The  volume  discharged  by  a  well  of  any 
size  will  depend  entirely  on  the  depth  of  the  well  and  the 
character  of  the  rock  in  which  the  water  is  found.  If  the 
rock  is  hard  and  fine  in  texture  the  flow  of  water  through  it 
will  be  less  than  if  the  rock  is  soft  and  coarse  and  filled  with 
pores  and  open  channels.  Again— the  volume  need  not  be 
great  because  the  pressure  is  high,  as  many  suppose.  This 
is  shown  by  a  comparason  o£  the  southern  with  the  north- 
ern wells.  The  southern  wells  having  in  some  cases  a  very 
large  flow  and  a  low  pressure  while  the  northern  wells  have 
a  lesser  volume  and  a  much  higher  pressure.  The  former 
are  not  so  deep,  either,  as  the  latter. 

When  the  well  is  closed  the  pressure  is  said  to  be  a 
STATIC  or  standing  pressure.  This  is  absorbed  in  throw- 
ing out  the  water  when  the  well  is  opened.  If  the  pipe  is  6 
inches  all  the  way  down,  more  water  will  get  into  the  bottom 
in  a  minute  than  if  the  opening  at  the  bottom  is  but  4 
inches,  and  that  at  the  top  6  inches,  yet  the  pressure  of  the 
water  will  be  the  same  when  closed  in.  So,  too,  the  rock 
may  be  so  hard  as  to  prevent  a  large  supply  reaching  the 
pipe  per  minute,  so  the  volume  will  be  small  although  the 
pressure  may  be  high. 

In  this  case  the  supply  fails  to  meet  the  duty  of  the  pres- 
sure. Other  wells  have  a  very  large  volume  and  compara- 
tively low  pressure.  In  this  case  the  rock  is  soft  and  open, 
permitting  of  a  large  and  free  flow  all,  or  only  a  part  of 


10 

which,  is  thrown  out.  The  condition  is  here  reversed,  •/.  e.. 
the  duty  of  the  pressure  tails  to  meet  the  volume  of  the  sup- 
ply. In  sinking  a  well  it  is  wholly  a  matter  of  conjecture  as 
to  what  the  volume  and  pressure  will  be.  The  chances  are 
in  favor  of  getting  a  larger  volume  from  a  larger  well,  but 
the  pressure  will  not  (as  above  explained)  increase  in  the 
same  proportion  as  the  volume;  nor  will  the  velocity  of 
discharge  keep  up,  under  a  given  pressure,  if  the  well  is 
larger  arid  the  volume  only  proportionately  greater. 

The  matter  of  relatiue  economy,  as  between  wells  of  differ- 
ent sizes,  has  yet  to  be  determined,  and  it  can  only  be  deter- 
mined by  the  sinking  of  many  wells  and  their  careful  study. 

In  other  countries  a  man  having  160  acres  figures  in  ad- 
vance on  just  what  water  he  needs  In  Dakota  a  man  fig- 
ures on  as  big  a  well  as  he  can  pay  for  and  is  hankful  for 
whatever  water  the  well  brings  him — the  more  the  better. 
In  figuring  on  what  kind  of  a  well  to  put  do  jvn  do  not  fig- 
ure too  fine,  that  is,  do  not  get  a  small  well  because  its  esti- 
mated volume  (judging  from  others  of  its  size  in  the  neigh- 
borhood) will  answer  your  purpose,  because  of  two  import- 
ant reasons . 

FIRST,  a  small  well  will  clog  or  stop  up  more  easily  than  a 
larger  one  and  will  be  more  costly  and  more  difficult 
to  clean  out. 

SECOND,  incase  of  accident  du'ing  the  drilling  or  after 
completion,  a  small  well,  may  be  spoiled  if  recased, 
while  a  larger  well  could  be  recased  and  still  leave  a 
serviceable  well.    The  smaller  one  might  have  to  be 
abandoned  under  circumstances  which  would  per- 
mit of  the  larger  well  being  rendered  serviceable. 
The  larger  well  has  thus  substantial  advantages  in  its 
favor  aside  from  the  mere  matter  of  volume,  and  a  few  dol- 
lars extra,  in  the  matter  of  cost,  ought  not  to  stand  in  its 
way.    The  increased  service  of  the  increased  volume  from 
the  larger  well  would,  in  many  cases,  pay  not  only  the  in- 
creased cost  but  for  the  whole  well. 

Stated  generally,  it  would  appear  to  be  poor  economy  to 
put  down  a  well  of  less  than  5  or  6  inches  diameter.  What 
the  economical  limit  above  this  size  will  be  remains  to  be 
demonstrated. 

Having  decided  upon  a  well,  of  say  6  inch  bore,  then  comes 
the  details  of  getting  it.  Some  will  contract  with  a  well- 
driller  near  at  hand;  others  will  advertise  for  bids,  and,  of 
course,  accept- the  lowest,  whether  it  be  best  the  or  not; 
others  will  seek  the  county  rig,  while  still  others  will,  either 
alone  or  by  clubbing  together,  buy  a  rig  and  drill  the  wrell 
themselves.  Some  will  f*vor  one  y  rpcess  and  some  another: 
while  some  will  favor  one  make  of  rig  which  another  person 
may  condemn. 

By  reason,  therefore,  of  this  diversity  of  circumstances, 
opinion,  and  preferences,  and  the  fact  that,  up  to  date,  very 


11 

little  systematic  work  has  been  done  and  no  one  process  or 
rig  has  demonstrated  its  superiority  over  all  others,  no  defi- 
nite instructions  can  be  given  as  to  the  best  course  to  pur- 
sue or  the  best  method  to  adopt.  If  a  CONTRACT  is  en- 
tered into  for  the  drilling  it  is  usually  as  a  result  of  bidding. 
In  this  case  the  chief  consideration  to  the  farmer  is  as  to 
size,  material,  cost  and  time,  and  not  as  to  the  method  or 
system  used  by  the  contractor.  He  may  use  poles,  cables,  or 
the  hydraulic  process,  as  he  prefers  so  long  as  he  gets  a  well 
111  proper  manner  and  time. 

The  details  of  the  contract  are  very  important  and  it 
should  be  drawn  up  by  some  one  who  understands  the  value 
and  importance  of  these  details,  so  that  there  is  contained 
all  that  should  be,  and  in  proper  form,  so  that  the  rights  of 
both  parties  will  be  protected. 

If  all  goes  well  the  contract  is  a  mere  ornament,  but  if 
trouble  arises  the  contract  comes  out  and  then  every  wor.d 
has  a  value.  The  contract  is  to  the  controversy  what  the 
safe  is  to  the  tire, 

From  the  information  contained  herein  it  is  expected  that 
any  man,  familiar  with  business  forms  and  customs,  may 
draw  up  his  own  contract  if  he  prefers  to  run  the  chance  of 
doing  it  properly. 

In  case  the  farmer,  alone,  or  associated  with  others,  de- 
sires to  do  his  own  work,  and  with  his  own  rig,  then  the 
choice  of  methods  and  rigs  enters  into  first  place  and  the 
matter  of  contract  is  eliminated. 

KINDS  OF  MACHINES.  As  previously  stated,  no  state- 
ment of  general  preference  will  be  risked.  Each  class  of 
machines  has  its  special  advantages  or  is  undoubtedly  the 
best  under  certain  circumstances.  The  conditions  of  drilling 
here,  however,  differ  from  those  of  most  other  sections.  Old 
eastern  drillers  declare  work  here  to  be  far  harder  than  work 
in  the  east  where  the  rock  is  more  solid,  where  the  casing 
may  be  omitted  in  many  or  most  cases,  and  where  the 
formations  are  better  known  and  understood.  Here  the 
formations  are  principally  shale  and  the  drilling  very  diffi- 
cult and  heavy  casing  always  necessary. 

POLE  MACHINES.  The  earlier  wells  in  Dakota  were  all 
drilled  by  pole  rigs,  that  is,  rigs  using  wooden  drill-rods. 
Aside  from  the  matter  of  time  taken  up  in  the  coupling  and 
uncoupling  of  the  rods  in  putting  the  tools  into,  and  taking 
them  from,  the  well,  these  rigs  have  proved  most  satisfacto- 
ry under  all  circumstances  and  have,  without  doubt,  per- 
formed the  best,  cheapest  and  most  rapid  work. 

The  uncoupling  of  the  rods  or  their  breaking  are  disad- 
vantages which  tend  to  frequent  accidents  but  these  risks 
are  largely  overcome  by  the  use  of  efficient  grappling x  tools 


1.2 

The  special  advantages  of  the  pole  rigs  lie  in  the  certainty 
of  their  drilling  action.  The  revolution  of  the  rods  is  uni- 
formly in  the  direction  of  tightning  the  screw  threads  of  the 
joints,  thus  aiding  in  preserving  the  tightness  of  all  the  con- 
nections. Again — the  rods  forming  a  rigid  connection  be- 
tween the  drill  and  the  hand  of  the  driller,  the  action  and 
'  position  of  the  drill  is  under  perfect  controll.  If  the  rods 
turn  it  is  certain  that  the  drill  turned  also  and  that  the  hole 
is  being  drilled  circular  and  not  oblong.  In  this  certainty  of 
control  over  the  action  of  the  tools  lies  the  chief  great  advant- 
age, in  this  state,  of  the  pole  rig  over  all  others.  Again— the 
rigidity  of  the  string  of  poles  makes  it  possible  to  tell  exact- 
ly where  the  bottom  of  the  hole  is  and  to  better  controll  tne 
blows  of  the  drill.  This  advantage  tends  further  to  an  in- 
crease in  the  number  of  blows  delivered  per  minute  for  the 
rods  have  greater  weight  than  the  cable 'ond  sink  more  rap- 
idly, the  friction  of  their  smooth  surfaces  is  less  than  with 
the  corrugated  surface  of  a  cable  and  the  rigidity  makes  it 
certain  that  if  the  upper  end  of  the  string  of  rods' sinks  that 
the  lower  end  has  done  the  same— there  being  no  kink,  or 
bending,  or  looping,  as  with  a  cable. 

CABLE  MACHINES.  Cable  rigs;  that  is,  rigs  using  eith- 
er rope  or  wire  cables  in  the  place  of  drill  rods,  are  very  large- 
ly used  now  because,  principally,  of  the  facility  of  operation. 
In  letting  down  the  tools  and  in  removing  them  much  time 
is  saved  by  having  a  continuous  run  instead  of  having  to 
stop  every  thirty  feet  to  couple  or  uncouple  a  rod  or  pole. 
The  danger  due  to  the  uncoupling  of  a  joint  is  done  away 
with,  In  these  features  lie  the  chief  advantages  of  the  cable 
rig.  The  disadvantages  are  many  and  well  worth  consider- 
ing. The  danger  of  breaking  the  cable,  under  strain,  or  if  a 
tool  becomes  fast,  is  greater  than  with  poles.  The  cable  is 
rotated  both  to  the  right  and  to  the  left  thus  making  it  pos- 
sible to  readily  uncouple  a  joint  at  the  tools,  if,  perchance, 
the  joint  became  loose  by  the  jar  of  the  drilling.  There  is 
danger  that  the  rotation  of  the  cable  will  not  always  cause 
a  corresponding  rotation  of  the  drill* and  the  hole  not  be 
drilled  truly  circular  thus  causing  trouble  in  sinking  the 
pipe.  This  is  especially  noticablein  the  important  operation 
of  reaming,  which  is  the  enlargement  of  the  hole  by  scraping 
away  its  sides,  an  operation  requiring  care  and  a  tool  so 
worked  as  to  cut  away  the  full  circle  and  not  merely  part  of 
it.  With  the  cable  the  rotation  may  have  the  effect  of  mere- 
ly twisting  the  rope  instead  of  rotating  the  tool.  With  the 
pole  rig  this  cannot  be.  Again,  when  the  hole  is  several  hun- 
dred feet  deep,  and  where  the  drilling  is  done  in  water  which 
may  be  flowing  out  with  considerable  velocity  and  pressure, 
the  velocity  of  the  drill  blows  must  be  slow.  If  the  motion  is 
rapid  the  walking-beam  returns  to  the  lifting  motion  before 
the  tools  have  had  a  chance  to  fall  and  drag  down  the  cable 
agaiESt  the  upward  motion  of  the  water. 


13 

In  this  way  the  energy  expended  may  be  absorbed  not 
iu  effective  drilling  but  in  merely  churning  on  the  cable. 
With  poles  this  is  otherwise,  as  explained.  On  occount  of 
these  manifest  disadvantages  several  drillers  have  abandon- 
ed the  use  of  cables  in  the  drilling  work  and  have  construct- 
ed what  are  called  "combination"  rigs,  that  is,  rigs  using 
poles  for  drilling  and  the  cable  for  operating  the  sand  pump, 
and  for  other  purposes  requiring  rapid  action.  This  ar- 
rangement has  proved  most  satisfactory  for  it  combines  the 
advantages  and  eliminates  the  disadvantages  of  both  rys- 
tems.  There  may,  in  the  cable  rigs,  be  a  choice  as  to  cables. 
]n  most  cases  the  2  inch  rape  is  used  because  it  is  cheaper 
than  wire,  but  the  wire  possesses  the  advantage  of  answer- 
ing all  the  conditions  of  stength  required  in  heavy  service, 
and,  it  is  said,  the  elasticity  of  the  wire,  when  under  the  ten- 
sion of  the  life,  aids  materially  in  the  important  operation 
of  twisting  the  drill,  thus,  to  a  great  extent,  neutralizing  the 
effect  of  possible  carelessness  on  the  part  of  the  driller. 

HYDRAULIC    OR     JETTING     MACHINES. 

These  rigs  are  of  many  patterns  and  workon  quite  dissim- 
ilar plans  but  all  pass  by  the  common  name  of  "jetting" 
or  "rotary"  rigs.  In  one  class  of  rig  the  drilling  is  done 
with  a  very  short  drill-bit  having  a  hollow  shank  through 
which  a  jet  of  water  is  forced  from  the  hollow  drill  rods 
« pipe-rods.)  This  creates  an  upward  current  which  car- 
ries out  the  drillings,  thus  doing  away  with  much  pumping 
and  permitting  the  almost  continuous  operation  of  the  drill. 
These  rigs  are  almost  untried  here  but  much  is  claimed  for 
them. 

The  rotary  hydraulic  rigs  are  among  the  latest  in  the  Da- 
kota field  and  hence  are  the  most  untried.  They  have  in 
other  sections,  and  especialy  in  the  shallower  wells  proved 
vastly  superior  to  other  rigs.  In  several  cases  here  they 
have  had  phenmoinally  successful  runs,  down  to  depths  of 
500  to  700  feet,  but  for  greater  depths  they  have  not  proved 
a  uniform  success,  yet  the  process  could  not,  in  most  cases, 
be  blamed  for  the  failure. 

Judging  from  the  very  nattering  successes  met  with  in  a 
few  cases,  one  may  safely  predict  a  very  wide  field  of  use- 
fulness for  these  machines,  and  especially  when  their  oper- 
ation in  our  peculiar  formation  is  better  understood.  Even 
these  rigs— like  both  the  pole  and  cable  rigs— are  already 
undergoing  the  ordeal  of  rearrangement  and  modification  to 
better  suit  them  to  the  conditions  here  met.  The  lastest  ad- 
vices are  to  the  effect  that  very  important  modifications 
have  but  recently  been  made,  by  the  American  Well  Works, 
which  promise  to  make  the  rig  as  nearly  suited  to  Dakota 
as  mechanical  ingenuity  can  at  present  approach. 

The  elements  of  watchfulness,  mechanical  ability,  quick 
and  accurate  judgment,  and,  above  all,  extreme  care  neces- 


14 

sary  to  success  with  any  rig  or  any  system  apply  particular- 
ly to  this  class  of  rigs. 

It  may  be  said  (as  the  result  of  ten  years  of  exper'ence 
and  observation  in  Dakota)  that  a  very  large  majority  ol  the 
.  many  accidents  in  the  well-drilling  operations  of  this  state 
have  been  due,  not  to  any  fault  in  the  process  or  the  rig,  but 
to  sheer  ignorance  or  carelessness  on  the  part  of  the 
drillers,  many  of  whom  have  been  without  knowledge  of,  or 
experience  in,  the  well  business,  hired  as  mere  helpers  yet 
placed,  often  times,  in  full  charge  of  the  work  and  with  no 
responsibility  as  to  its  safe  and  proper  conduct 

This  being  undeniably  true,  it  may  be  further  stated  that 
the  exercise  of  care  and  judgment  is  of  more  importance 
to  the  owner  of  a  rig  than  the  mere  mechanical  details  of 
the  rig  itself;  for  a  poor  tool,  in  the  hands  of  an  expert,  will 
do  better  work  than  a  fine  tool,  in  the  hands  of  a  careless 
and  ignorant  ivorkman. 

TOOLS. 

In  the  selection  of  drills,  reamers,  pumps,  grappling- 
tools  and  other  accessories  of  a  drilling  outfit  select  with 
reference  to  the  size  and  style  of  the  rig,  and  in  matters 
of  detail  rely  upon  the  advice  of  some  responsible  manufac- 
.  turer ;  bearing  in  mind  one  thing— get  enough  tools.  Do  not 
work  "short  handed,"  for  it  will  not  pay  in  the  well  business. 

If  a  rod  or  cable  breaks,  or  a  tool  is  dropped  into  the  well, 
be  prepared  to  handle  the  case  AT  ONCE,  for  any  delay 
may  cost  hundreds  of  dollars.  Have  the  tools  to  treat  all 
cases,  have  them  where  they  belong,  and  don't  allow  a  meal. 
a  circus  or  even  cold  or  darkness  to  interfere  with  prompt 
action  and  invaribly  leaving  the  work  so  it  is  safe. 

Be  prepared  for  accidents  for  they  are  sure  to  come ! 

The  machinery  having  been  selected,  and  the  well  begun, 
the  nest  consideration  is  as  to  the  pipe. 

PIPE. 

LAP-W£LD.  The  selection  of  a  suitable  pipe  is  a 
matter  of  importance  upon  which  de- 
pends, very  largely,  the  success  or  the 
failure  of  the  well.  In  the  past,  pipe  of 
Ull  sorts  of  makes  and  weights  has  been 
[used,  and  with  varying  success. 

Wrought  iron  pipe  is  of  two  classes— 
the    BUTT-WELDED    and     the    LAP- 
WELDED.    Fig.  1  shows  the  great  differ- 
ence between  these  welds,  and  the  super- 
BUTT-WELD.    ior  strength  of  the  lap-weld  which   h  s 
Fig.  1.  about  4  times  as  much  surface  in  contact 

at  the  weld  as  is  had  in  the  butt-weld. 

It  is  clear  that  butt-welded  pipe  would  not  be  safe  to  use 
in  our  wells,  yet  some  hns  been  used  and  with  disastrous 
effect. 


15 

All  pipe  should  be  lap- welded . 

The  thinner  the  pipe  the  shorter  and  weaker  is  the  weld; 
the  thicker  the  pipe  the  longer  and  stronger  is  the  weld. 
Wrought  iron  pipe  (like  most  other  things  these  days,)  is,  in 
its  different  classes,  made  on  standard  models;  that  is,  the 
thickness,  area,  weight,  etc.,  per  foot,  for  any  given  size  will 
vary  but  little  as  between  different  makers,  and  certain 
standard  brands  are  listed  by  nearly  all.  Thus,  there  is 
what  is  known  as  ''Standard"  pipe,  x  or  extra  strong,  xx  or 
double  extra  strong,  casing  pipe,  line  pipe,  drive  pipe,  tub- 
ing, etc. 

Most  of  these  brands  will  not  be  used  here.  The  standard 
pipe  is  that  which  is  commonly  used  and  is  a  brand  suffici- 
ently heavy  for  every  use  unless  it  be  that  of  very  heavy 
driving  for  which  purpose  drive-pipe  is  designed,  it  being 
of  a  better  grade  of  iron  and  hence  stronger.  For  lighter 
work— as  for  the  casing  used  in  starting  a  w  11,  or  the  pipe 
used  in  recasing  an  old  well — the  lighter  or  casing  pipe  is 
the  grade  used. 

Table  No.  1,  on  the  next  page,  gives  the  dimensions, 
weights,  etc.,  of  "Standard"  pipe. 

Some  drillers  are  of  the  opinion  that  drive  pipe  should  be 
used  in  all  Dakota  well  work  because  of  the  liability  of  get- 
ting the  pipe  fast  and  being  obliged  then  to  subject  it  to 
very  heavy  driving,  or  pulling  with  jack-screws,  in  order  to 
loosen  it.  There  is,  of  course,  much  ground  for  this  opin- 
ion and  it  goes  without  proof  that  if  the  stronger  pipe*  is 
used  the  well  will  be  the  better  for  it  and  the  operation  of 
sinking  it  the  safer;  but  it  were  useless  to  use  heavier  pipe  if 
a  lighter  grade  would  answer  every  purpose. 

The  opinion  is,  therefore,  repeated  that  if  the  drilling  and 
reaming  are  properly  and  sufficiently  done,  the  "standard" 
grade  of  pipe  will  serve  every  purpose,  at  any  rate  in  wells 
of  8  inches  or  less  in  size.  The  wrear  and  tear  on  the  pipe  is 
greatly  lessened  by  sufficiently  reaming  out  the  hole  under 
the  pipe,  by  the  use  of  expansion  or  other  reamers.  Fre- 
quently this  is  overlooked,  or  insuffiiently  done,  and  the 
pipe,  after  hard  driving,  becomes  fast  and  days,  or  even 
weeks  of  delay  are  consumed  in  an  effort  to  loosen  it  and  to 
do  over  again' what  should  have  have  been  done  well  in  the 
first  place.  Too  great  care  cannot  be  used  in  this  part  of 
the  work.  If  the  reaming  is  well  done  the  pipe  will  settle 
easily  and  rapidly,  or  with  but  light  driving,  and  a  lighter 
grade  of  pipe  might  safely  be  used;  but  if  the  reaming  is  in- 
sufficiently done,  and  heavy  driving  resorted  to,  then  stand- 
ard or  drive  pipe  should  be  used. 

It  shauld  be  noted  that  the  external  diameters  of  pipe 
must  remain  the  same  in  order  to  fit  to  standard  couplings. 
If  the  pipe  is  made  heavier  ttie  extra  metal  is  added  to  the 
inside  and  the  internal  diameter  thereby  reduced. 

*Drive  and  line  pipes  are  of  standard  sizes  and  weights,  but  being:  of  a 
better  grade  of  iron  they  arc  stronger  and  more  expensive. 


16 
TABLE  NO.  1. 

READING   IRON   COMPANY. 


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TABLE  NO.  2. 
READING  TROX  COMPANY. 


^STANDARD. 


WROUGHT  IRON  LAP-WELDED  PIPE, 

FOR  STEAM,  GAS,  AND  WATER. 

MANUFACTURERS'   PRICE   LIST. 
REVISED  AND  ADOPTED  SEPT.   18,   1889. 

To  take  the  place  of  all  previous  lists  and  subject  to  change 
without  notice. 


Nominal 
Inside 
Diameter. 

Price            Price           Nominal 
per  Foot,    per  Foot,       Weight 
Plain.      Galvan'z'd     per  Foot. 

Thickness. 

No.  of 
Thread  pet- 
inch  of 
screw. 

Inches. 
'# 

$        c.         $       c.            Pounds. 

.23           .26          2.68 

Inches. 
•H5 

"X 

2      • 

•30           -34          3-°i 

.154 

H/z 

*/2 

•47    i       -53          5-74 

.204 

8 

3 

.62 

.68          7.54 

.217 

8 

3</2 

•74 

.88          9.00 

.226 

8 

4 

.88 

1.03         10.66 

-237 

8 

4^ 

i.  06 

I-31         I2-34 

.246 

8 

5 

1.28 

i.  60 

14.50 

.259 

8 

6 

1.65 

2.00 

18.76 

.280 

8 

7 

2.10 

23.27 

.301 

8 

8 

2.75 

28.18 

.322 

8 

9 

3-75 

33-70 

•344 

8 

10 

4-75 

40.06 

.366 

8 

ii 

6.00 

45.02 

•375 

8 

12 

7.00 

49.00 

•375 

8 

13 

8.00 

54-00 

•375 

8 

14 

9.50 

5800 

•375 

8 

15 

11.00 

i      62.00 

•375 

8 

Prices  of  Standard  Pipe. 

Discount  on  galvanized  pipe  about  55  per  cent. 
"         "       plain         "         "     62^     "       " 
(See  table  No.  3.) 

The  same  prices  are  quoted  by  all  makers  and  as  the  mar- 
bet  price  fluctuates  the  rate  of  discount  changes.  Current 
discounts  can  be  had  from  the  makers.  Those  given,  here- 
in are  not  the  latest  but  will  fully  answer  the  purpose  of  ap- 
proximate estimates. 

For  selected  pipe,  or  pipe  cut  to  special  length  the  dis- 
count is  usually  5  per  cent.  less. 


18 
TABLE  XO.    3. 

The  following  prices  ai%e  also  quoted. 
NET   PRICES. 


Size  of  pipe.       Tubing. 

Line  pipe.  Drive  pipe. 

Standard  pipe. 

IV*  inch  os.                  .12 
2                                    .14 
2U                                 .19 
3                                  .  2* 
3^4 

.OSH 

4114 

-  IT'/z 
.22V4 
.27%. 
.33 
.  39^ 
.48 
.60% 
.78% 
1.07 
1.40H 
L.78 
2.62 

-£  c 
§"5s 

^~ 

SBj 

••>$?  OD  cS 

II| 

~  ^L 

^S 
d  *  eS 

|a-i 
||.§ 

3  S'E 

.12 
.17 
.21 
.26 
.30 
36 

.28 

4                                 .39 
4U                    

.40 

r>                      

.44 

.56 
.72 
.90 
1  30 

"".76"' 

7                         

s 

1.20 

9 

10 

1  55 

1.95 

2.53 

12 

2.30 

This  table  is  arranged  so  as  to  show  comparative  prices  of 
different  grades  of  pipe.  The  prices  for  standard  pipe  being 
the  net  prices  resulting  from  the  discount  and  list  prices 
given  in  table  2,  for  plain  pipe. 

The  prices  here  given  will  fully  answer  the  purpose  of  es- 
timate. Exact  prices  can  only  be  Lad  by  correspondence 
with  the  manufacturers,  who  will  quote  the  latest  lists  and 
discounts. 

That  feature  of  the  pipe  which  is  of  the  greatest  eonsern 
to  the  well  driller  is  the  thread  and  it  is  chiefly  on  account 
of  the  thread  that  heavier  pipe  is  needed.  If  the  pipe  is  thin 
and  light  so  much  of  the  body  of  the  metal  is  cut  away  in 
the  operation  of  threading  as  to  leave  a  thin  shell  not  suffi- 
ciently strong  to  withstand  the  driving  blows  without  dan- 
ger of  stripping  the  thread. 

If  the  pipe  is  heavy  the  body  of  metal  back  of  ^he  threads 
is  stronger  and  the  pipe  therefore  more  able  to  withstand 
heavy  work. 

COUPLINGS.     (See  table  No.  7.) 

The  common  form  of  coupling  is  straight  threaded,  that 
is,  the  line  of  the  threads  is  parallel  to  the  outer  surface  of 
the  coupling.  An  improved  form  gives  greater  strength  to 
both  pipe  and  coupling  and  distributes  the  strain  more  even- 
ly over  the  line  of  the  thread.  This  is  known  as  the  patent 
TAPEH  COUPLING.  From  the  illustrations  of  this  form 
of  coupling,  shown  in  connection  with  the  advertisements 
on  the  front  and  back  covers  and  by  Fig.  2  on  page  20..  it 
will  be  seen  that  the  inner  face,  or  threaded  surface  of  the 
coupling,  has  the  form  of  a  funnel  to  fit  a  corresponding 
conical  taper  on  the  pipe.  In  drive-pipe  the  ends  of  the 
pipe  meet  at  the  middle  of  the  coupling. 


19 
TABLK  NO.  4. 

READING  1RO\T 


X  STRONG  AND  XX  STRONG 

WROUGHT  IRON  LAP-WELDED  PIPE. 

X  STRONG. 


Actual          Nominal                               Nominal 

Size. 

rnce 
per  Foot. 

Outside            Inside 
Diameter.      Diameter. 

Thickness.       Weight 
per  Foot. 

Inches. 

$    c. 

Inches.           Inches. 

Inches. 

Pounds. 

11A 

.46 

I.9O 

1494 

.203 

3-63 

2 

.60 

2-375 

1-933 

.221 

5.02 

2X 

•94 

2.875 

2315 

.280 

7-67 

3 

1.24 

3-5° 

2.892          .304 

10.25 

1.48 

4.00 

3-358          .321 

12.47 

4 

1.76 

4-5° 

3.818          .341           14-97 

4^                2.12 

5-              4-25            -35            J7-6o 

5             2.56 

5.563        4.813          .375 

20-54 

6              3-30 

6.625    !     5.750 

•437 

28.58 

7               4-20 

7.625        6.62 

.50 

37  60 

8 

5-50 

8.625        7.50           .56           47.85 

XX  STRONG. 


Actual 

Nominal 

Nominal 

Size. 

Price 
per  Foot. 

Outside 
Diameter. 

Inside 
Diameter. 

Thickness. 

Weight 
per  Foot. 

Inches. 

$     c. 

Inches. 

Inches. 

Inches. 

Pounds. 

11A 

.92 

1.90 

1.088 

.406 

6.40 

2 

1.  2O 

2.375 

I.49I 

.442 

9.O2 

2l/2 

1.88 

2.875 

1-755 

.560 

13.68 

3 

2.48 

3-50 

2.284 

-   .608 

18.56 

2.96 

4.OO 

2.716 

.642 

2275 

4 

4-50 

3136 

.682 

2748 

4^ 

4.24 

5- 

3-56 

.72 

32.45 

5 

5.12 

5-563 

4.063 

•75 

38.12 

6 

6.60 

6.625 

4.875 

.875 

53" 

7 

8.40 

7.625 

5.98 

.82 

60.34 

8 

11.00 

8625 

6.88 

-87 

71-52 

Discount  about  62  J^  per  cent. 
Xot  the  most  recent  quotation. 


20 
TABLE  NO   5.        CASING,  NET  PRICES. 


Nominal 

Actual              Nominal 

No.  Threads 

Inside 

Price 

Outside              Weight 

Per  Inch 

Diameter. 

Per  Foot. 

Diameter.         Per  Foot. 

of  Screw. 

3*                      20 

3i                4.27 

14 

3*                    21                   3f                   4.6o 

14 

3?                   24                  4                     5-47 

14 

4 

25 

4i                     5-85 

H 

4T 

27 

4^                   6.00 

H 

4i 

35 

4!                    9.00 

H 

4f 

3° 

4¥                   6.  50 

14 

4f 

36 

4^                    9.00 

14 

4§ 

33                  5 

7-58 

14 

5 

35 

Si 

8.00 

J4 

5 

41                  Si 

1000 

14 

5 

48 

si 

13.00 

iij 

•5^ 

58 

si 

17.00 

u| 

5  16 

39 

si 

8.50 

H" 

•  Sfe 

50 

5l 

13.00 

n| 

5f 

45 

6 

10.00 

14 

51 

5° 

6 

12.00 

n| 

5l 

55 

6 

I4.OO 

n| 

1 

59 
64 

6J 

11.15 
13.00 

H" 
H 

65 

74 

6f 

17.00                         III 

6f 

68 

7                    !3oo                 14 

6f 

78 

7                   17.00                ii| 

83 

8 

I5.OO                         Il| 

7l 

95 

20.00                        Il| 

84 

95 

8^ 

16.15                         III 

8 

1.05 

8f 

20.00                         Il| 

i  15 

8f                24.00                n| 

8|     . 

1.  00 

9 

18.00                ni 

9l 

1.25 

10 

21.00                       H^ 

10  inch  Light  Pipe  for  Well  Purposes  ..............................  Net,  1.50 


As  made  by  the  Oil  Well  Supply  Co.,  Pittsburg, 

Fig.  2  shows  sections  of  pipe  joints  and  the 
ferred  to  on  P.  18.  Fig.  2. 


,  Penn.—  See  advertisement 
patent  taper  coupling   re- 


PATENT 
FLUSH  JOINT. 


SLEEVE    COUPLING. 

INSERTED  JOINT. 


21 

EXPLANATION  OF  FH;.  3. 


A.  Alain  pipe  of  well. 

B.  Gate  valve. 

C.  Hand  wheel  to  valve. 
Cms*,     the    openings    of 

which  may  all  be  of  one 
size  or  may  all  be  differ- 
ent. State  sizes  desired. 
Plugs,  for  closing  dead 
openings.  The  tops  may 
vary  as  shown. 

K.     Bushing,  for  reducing  size 
of  openings. 

Nipples,  for  connecting 
specials,  being  short  piece 
of  pipe  threaded  part  way 
or  all  the  way  and  being 
of  any  length  desired. 
Curved  tee,  just  the  form 
for  top  of  pipe.  Especial- 


for  top  of  pipe.  Especial- 
ly where  well  is  used  for 
power. 

I.    Plug,  plugged  for  gauge. 

J.    Pressure  gauge. 

L.    Reducer. 

L.     Elbow,  can  be  had  to  any 

angle. 

M.    Double  elbow. 
N.    Straight  tee,  can  be    had 

of  any  form  or  rize. 
O.    Reducing  tee.  can  be  had 

of  any  form  or  size. 


Fig.  3.    Specials  and  fittings  for  pipe 

TABLE 

TABLE    OF    COMPARATIVE    WEIGHTS 
IRON 


(See  page  21 ».  i 

NO.   6. 


OF   DIFFERENT    KIXUS     OF    WROUGHT 
PIPE. 


Size  of 
pipe. 

Casing 
pipe. 

Standard  j        X. 
pipe.      (Strong 

p  '                         Drive  pipe. 

2 

2.23!          3.61J          3. 

63 

3 

3.95 

5.74         7. 

67 

3^ 

4.27 

7.54       10. 

25 

Drive    mue      is  of    standard 

4 

5.33 

9.00 

12. 

47         weight  and  size   but  more  expen- 

4^ 
5 

6.00 
7.25 

10.66 
12.34 

14. 
17. 

cj~         sive,  stronger  and  better  on  ac- 
X,-.         count  of  its  being  made  of  a  bet- 
ter quality  of  iron.    Then,    too. 

5M 

7.66 

the  threads  are  cut  longer  to  fit  a 

5J£ 
6 

?>% 

8.08 
9.35 
10.06 

14.50 

20. 

54 

longer  and  stronger  coupling  (see 
table  7)    and  of  sufficient  length 
to  permit  the  ends  of  the  pipe  to 
butt    together    when    coupled  — 

i8.  76       28. 

58 

12  45 

this  it  not  the  case  in  standard 

f 

13.50 
15.10 

23.27       37. 

60 

pipe  —  thus  very  greatly  adding  to 
the  strength    of  the  pipe  in   the 
operation  of  heavy  driving,  the 

*% 
9 

16.15 
17.25 

28.18 

47. 

Sg 

pipe  being  practically  continous 
and   not  separated    at  each  joint. 

9% 

33  70 

ture  of  drive  pipe 

10 

20  00 

10% 

40.06 

Size— outside  diameter,  weights— pounds  per  foot. 


2*2 

TABLE  NO.  ". 

Dimensions  of  Wrought  Iron  Couplings. 


FOR   STANDARD  PIPE. 


Inside  diam. 
of  the  pipe.    2       212 

0 

3U    4 

11  ^    -j 

1)           7           N 

9 

10 

Outside  dia  . 
of  coupling.    278;  3aH7 

4 

W  5A 

•>i,\   8*4 

^l7,;     8  £2      9 

V        lOH" 

UH 

Length  of 
coupling.      2&j  3}  a 

3ft 

35S:     3?-8 

:;  •,    i       i 

6ft 

6ft 

FOR  LINE  PIPE,  DRIVE  PIPE   AND   TUBTM;. 


Inside  diam. 
of  pipe. 


Outside  dia. 
of  coupling.    23?,     3^      4jg 

4B 

^!s:  :,»  615 

Length  of 

coupling. 


6ft 


FOR  CASING  PIPE. 


Inside  diam. 
of  casing. 


4 


Ouiside  dia . 
of  coupling.    2  3. 


Length  of 
coupling. 


|  3T]5 


TABLE  NO.  8. 

Dimensions,  &c.  of  Special,  Lap-  Welded, 

KALAMEIN    PIPE, 

for  water  and   gas    works, 

As  made  by  the  National  Tube  Works  Co.,  Chicago. 


Outside 
diam  . 

Weight   of 
lock  joint. 

Wf.io-hfr*f     i      Nominal 
le»^e.»X^ 

Aproximato 
price  per  foot. 

Inches. 

Pounds  . 

1 

Pounds.              Pounds. 

$      Cts. 

2                  4 

1                       1.80 

.17 

3 

8 

1%              3.35 

.30 

4 

12 

2^              5.00 

.42 

5 

17 

3%              "  •  15 

.55 

6 

21 

5                  8.60 

.67 

7 

30 

6 

11.25 

.87 

8 

33                     6^ 

12.80 

1.00 

9 

38 

1U 

15.10 

1.25 

10 

40                     8" 

16.60 

1.45 

11 

50                    10^ 

20.  H5 

1.70 

12 

56 

11% 

24.50 

1.87 

13 

65 

12K' 

27.60 

2.2^ 

14 

71 

13M 

30.00 

2.50 

15 

100 

15% 

36.40 

2.80 

16 

120 

17 

46.25 

3.30 

TABLE  XO    1). 


TABLE  SHOWING  RELATIVE    AREAS  OK   STANDARD 


PI  ri:. 


Size 

«.f                 •=; 

Pipe. 

1     1', 

-        -'*         :5        :{'-: 

I 

28.10 

16.00 
7.11 
4.00 
2.56 
1.77 
1.30 
1.00 

44.4 

25.00 
11.10 
6.25 
4.00 
2.77 
2.04 
1.56 
1.00 

6 

87.10 
49.00 
21.70 
12.25 
7  M 
5.44 
4.U; 
3.08 
1.96 
1.81 
1.00 

> 

113.70 
64.00 

28.40 
16.00 
10.21 
7.11 

4  '.00 
2.56 
1.77 
1.30 
1.00 

!!             1.011 

1 

V-    •" 

:^ 
H'.> 

1.774.00 

1.00  2.25 
...    UK) 

7.11  11.10  16.0021.70 

4.IM)    6.25    9.00  12.20 
1.77    2.77    4.00    5.44 

i.oo   i.56   2.25   3.<H> 
....     1.00,  1.44    1.96 
....  1.00    l.Sl 
i  1.00 

64.00 
36.00 
16.00 
9.00 
5.76 
4.00 
2  93 
2.25 
1.44 
1.00 

r> 

- 

s           .... 

!  i  1  

i  

From  Win.  J.  Baldwin,  M.  E.  in  "Steam  Heating  for  Buildings." 

Explanation  of  table:  The  relative  areas  of  any  two 
sizes  of  pipes  given  in  the  table  will  be  found  at  the  inter- 
section of  the  horizontal  and  vertical  lines  representing  the 
given  sizes.  Thus,  a  6-inch  pipe  —  1.00  6-inch  pipe,  1.44  5- 
inch  pipes  and  4  3-inch  pipes;  an  8-inch  pipe  —  4  4-inch 
pipes,  16  2- inch  pipes,  113.7  %-inch  pipes,  etc. 

Application— It  is  desired  to  supply  50  three  quarter  inch 
pipes  with  a  constant  flow,  what  size  of  supply  pipe  should 
be  used  ?  Take  top  horizontal  line  and  run  to  the  right,  it 

will  be  seen  that  a  5  inch  main  will  supply  but  44.4 % 

inch  pipes;  but  a  6  inch  main  will  supply  64.00 %  inch 

pipes,  hence,  a  6  inch  pipe  must  be  used.  An  8  inch  well  is 
as  large  as  7.11  three  inch  wells,  a  7  inch  well  as  large  as 
3.06 ....  4  inch  wells. 

As  to  Relative  Dircharging  Powers  of  Pipes,  see  Table 
No.  27. 

TABLE  NO.  10. 

WEIGHT  OF   STANDARD  CAST  IRON  PIPE. 

(Including  Bowl  and  Spigot  ends.) 
( 'ast  iron  weighs  450  Ibs.  per  cubic  ft.  and  .26041bs.  per  cubic  inch. 


Diam. 
of 
Pipe. 

Weight  per  foot  for  following  thicknesses. 

Length 
Feet. 

H 

H 

% 

'/2 

% 

% 

% 

1 

.     2 
3 
4 
5 
6 
8 
10 
12 

3 
4 
5 
6.5 
8 
10 
14 
15 

6 
9 
11 
13.5 
16.5 
21.5 
27. 
32 

9.3 
13 
17 
21 

25. 
32.5 
40.5 

48 

14 

18 
23.5 
29 
34 
44 
55 
65 

19 
23 
30 
36 
43 
56 
69 
82 

29 
37 

45 
53 

68 
84 
100 

44 
53 
63 

81 
99 
117 

52 
62 
73 
93 
114 
135 

8 
12 
12 
12 
12 
12 
12 
12 

As  made  by  Addyston  Pipe  &  Steel  Co.  (See  adv't  P.  216.) 

This  table  incudes  all  of  the  sizes  and  weights  likely  to 
find  a  place  in  water  and  gas  works  plants  in  Dakota,  where 
the  use  of  cast  iron  for  water  works  is  on  the  increase.  * 

(See  also  the  advertisement  of  Dennis  Long  &  Co.  P.  217.) 


24 
TABLE  NO.  11. 

DIMENSIONS,  PRICE,  ETC.,  OF  SPIRAL  RIVETED  PIPE. 

No.  18  Wire  Guage.  Thickness  .049  inch. 


Diam.  in 
inches. 

Price  per 
ft.  Black. 

Price,  tar- 
red and 
asphalted. 

Price  per 
ft.  Galvan- 
ized. 

Approx. 
weight  per 
100  feet. 

Approx. 
bursting 
pressure 

NET. 

NET. 

NET. 

Ibs. 

Ibs  per  sq  in. 

3        !8      .17 

8      .19 

&       23 

185 

1300 

4 

.21 

.23 

.29 

245 

1000 

5 

.25 

.28 

.35 

300 

800 

6 

.29 

.32 

.43 

360 

700 

7 

.32 

.35 

.45 

400 

600 

8 

.37 

.40 

.52 

460 

500 

9 

.41 

.45 

.59 

525 

450 

10 

.45 

.50 

.65 

575 

400 

11 

.48 

.53 

.70 

625 

360 

12 

.58 

.64 

.82 

750 

330 

13 

.62 

.69 

.90 

800 

300 

14 

.67 

.75 

.98 

900 

280 

15 

.75 

.83 

1.05 

950 

260 

16 

.80 

.88 

1.13 

1000 

250 

18 

.88 

.96 

1.28 

1125 

220 

20 

1.00 

1.10 

1.45 

1250 

200 

22 

1.10 

1.21 

1.55 

1350 

180 

24 

1.20           1.32 

1.67           1460 

160 

In  lengths  of  25  feet  and  less,  with  plain  or  crimped  ends. 
As  made  by  Abendroth  &  Root  Mfg,  Co.     (See  adv't  P.  238.) 
The  weights  given  are  for  the  black  pipe,  other  grades  are  from  10  to  20 
per  cent,  heavier. 

This  class  of  pipe  is  very  extensively  used  in  the  west  for 
conveying  irrigation  waters,  and  in  many  places  for  water 
works  use.  Its  strength  is  very  great  while  the  weight  is 
very  light,  and  the  cost  low.  On  account  of  its  strength, 
lightness  and  cheapness  it  will  be  especially  adapted  to  use 
in  Dakota,  where  water  must  be  piped  on  or  near  the  sur- 
face. 

The  following  table  will  show  the  comparative  weight  of 
the  three  classes  of  pipes— Spiral,  Standard  wrought  iron 
and  Cast  iron: 

WEIGHTS. 

Heaviest  Spiral                  Standard  Wrought  Cast  Iron 

Pipe.  Iron  Pipe. Pipe,  %  inch 


4    * 
6    ' 
8 
10 
12 
14 
16 
18 
20 

24 

...-2V2 

10^£   "                         17 

18%     '              25 

....8 
.  ..10 
...13 
...15 
...18 
...20 
•)2 
.'..'24 
...26 

28        «                         32 

40        '  ..              40 

49        <                 48 

58        c  56 

64 

...72 

79 

...95  " 

Pipes  of  this  class  in  California  have  been  in  use  since  1853  and  hav 
given  great  satisfaction,  many  having  done  useful  service  for  25  and  3 
years. 

25 
TABLE  NO.  12 

READING  IRON  COMPANY. 


•£•£  £ 

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"f    w£   ^K            H» 

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LU 

c£ 

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00 

n 

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QJ 

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Number  of 
gauge. 

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26 

Inadvertently  the  text  for  this  page  was  overlooked  but 
two  suggestions  may  be  here  inserted  with  profit,  no  doubt, 
to  some. 

The  first  suggestion  is  prompted  by  the  abundant  rain-fail 
of  the  early  months  of  1892  which  has  been  far  greater  than 
that  of  any  former  year  within  the  history  of  the  state. 
Some  are  heard  to  say  that  "irrigation  will  now  be  overlook- 
ed." Such  will  not  and  should  not  be  the  case,  for,  al- 
though 1892  may  be  a  year  of  great  productiveness  without 
irrigation,  it  will  still — however  good  it  may  be — fall  far 
short  of  accomplishing  what  irrigation  would  accomplish. 

Through  any  given  series  of  years  Dakota's  rain-fall  can- 
not be  relied  upon  to  be  sufficient  for  remunerative  farm- 
ing; so  irrigation  must  be  resorted  to  by  all  who  desire  cer- 
tainty of  return  for  each  season's  labors.  If  all  who  can 
will,  during  this  favorable  season,  prepare  for  the  unfavor- 
able seasons  which  are  sure  to  come,  they  will  exercise  wise 
forethought  by  hastening  to  improve  the  opportunity  so 
fortunately  offered  of  preparing  in  advance.  This  promis- 
ing season  will  no  doubt  aid  many  financially  to  in  whole  or 
in  part  prepare  for  irrigation  in  the  future. 

It  is  said  of  an  Arkansas  farmer  that  he  refused  to  mend 
his  leaky  roof  during  fair  weather  because  it  was  not  neces- 
sary, and  during  foul  weather  he  couldn't  because  it  was 
wet.  It  is  hoped  that  our  farmers  will  not  emulate  such  un- 
thrift  by  refusing  to  prepare  for  irrigation  during  wet  sea- 
sons, because  it  is  then  unnecessary,  and  being  compelled  to 
put  it  off  during  dry  seasons  because  too  poor. 

A  second  suggestion  will  be  risked,  although  somewhat 
outside  of  the  scope  of  this  work.  It  is: 

Do  not  be  deceived  by  so-called  Rain  Makers !  Do  not  fol- 
low so  intangible  a  will-o-the-wisp  as  this  latest  "fake"  with 
which  scheming  sharpers  are  attempting  to  delude  the  peo- 
ple. The  U.  8.  government  spent  several  thousand  dollars 
in  a  vain  attempt  to  produce  rain;  an  attempt  which  was  an 
acknowleded  failure,  except  that  it  awakened  in  the  breasts 
of  certain  shapers  an  idea  which  they  have  enshrouded  in 
mystery,  and  on  the  strength  of  which  they  seek  to  extort 
money  from  a  too  credulous  public.  Bain-making  has  not 
been  a  success  as  yet— we  hope  it  may  be  in  the  future. 

Water  we  have  below  us.  We  know  it  is  there,  and  that 
we  can  get  it.  Seek  it,  therefore,  and  do  not  delay  in  the 
vain  hope  that  the  secret  of  rain-making  has  been  vouchsaf- 
ed to  men  of  whom  the  world  has  never  heard,  men  un- 
known in  the  sphere  of  science,  men  whose  investigations 
were  never  heard  of  and  whose  successes  are  but  hearsay  or 
newspaper  reports,  men  who  want  pay  in  advance  and  will 
not  exhibit  the  powers  which  they  claim  thus  suddenly  to 
have  acquired  to  the  light  of  scientific  investigation;  men 
who  work  in  the  dark  and  who  seek  their  own  interests  and 
not  yours.  Some  wit  has  wisely  said  that,  as  yet,  "the  har- 
ness-maker is  the  only  successful  rein  maker." 


SPIRAL  WELDED  PIPE. 

This  pipe  is  very  similar  to  the  spiral  riveted  pipe,  the 
joint  being  welded  instead  of  riveted.  The  weights  are 
about  the  same  as  the  weights  of  riveted  pipe,  but,  by  reason 
of  the  welded  joint,  the  pipe  is  claimed  to  be  stronger,  more 
durable,  smoother  internally.  Both  possess  the  same  great 
advantages  of  lightness  and  cheapness  and  are  equally  well 
adapted  to  use  in  irrigation  whenever  a  light,  durable  and 
inexpensive  pipe  can  be  used.  (See  distribution  of  water, 
P.  122.) 

From  the  foregoing  tables  it  will  be  possible  to  select  a 
quality  or  kind  of  pipe  suited  to  the  needs  of  the  well,  the 
water-Works  plant,  or  the  conveyance  of  water  over  the 
surf  ace  for  irrigation .  More  detailed  information  maybe 
had  by  correspondence  with  the  manufacturers  or  dealers  in 
pipe  whose  advertisements  appear  herein. 

The  proper  grade  of  pipe  having  been  selected,  the  plan  of 
the  well  must  be  decided  upon,  for  it  may  be  on  several 
plans. 

A  large  outer  casing  may  be  first  used  and  sunk  as  deep 
as  thought  desirable,  then  a  smaller  size  sunk  inside  of  the 
first,  and,  possibly,  still  a  smaller  size  within  the 
second  pipe;  the  latter  being  carried  to  the  bot- 
tom. The  two  outer  pipes  may  then  be  pulled 
up,  leaving  a  continuous  pipe  from  top  to  bot- 
§  torn.  In  some  cases,  as  where  the  outer  casing  has 
become  fast  and  cannot  be  lifted,  the  outer  pipe 
is  left  in  the  well  thus  making  a  double  string 
of  pipe.  In  other  cases,  all  the  outer  casing  is 
removed,  but  2  or  3  lengths,  the  space  between 
the  two  casings  being  then  calked. 

In  some  wells  the  telescope  plan  is  used,  In 
this  case  the  well  may  start  with  an  8  inch  pipe 
carried  down  say  300  feet;  then  a  6  inch  pipe  is 
carried  down  say  400  feet  lower,  or  to  a  depth  of 
700  feet,  and,  by  the  use  of  a  left-handed  thread 
at  the  300  foot  level,  the  upper  300  feet  of  the  6 
inch  pipe  is  removed,  leaving  the  lower  400  feet 
in  the  well  as  permanent  casing.  In  like 
manner  a  4J^  inch  pipe  may  be  sunk  within  the 
six  inch  pipe  and  carried  to  water;  the  upper 
700  feet  being  then  removed.  Such  a  well,  in 
section,  would  have  the  appearance  shown  in 
Fig.  4. 

Most  of  the  earlier  wells  were  of  this  class 
and  many  are  still  drilled  on  this  plan,  but  the 
practice  now  appears  to  tend  more  in  the  direc- 
tion of  wells  with  a  continuous  line  of  pipe  from 
top  to  bottom,  and  such  wells  no  doubt  have 
many  marked  advantages  over  wells  of  other 
classes. 

Fig.  4. 


torn  of  the  well. 


PERFORATED  PIPE. 

Nearly  all  of  the  northern  wells  throw  out  more  or  less 
shlae  mud,  clean  sand,  or  lumps  of  sand-rock  or  iron  pyrites. 
These  hard  bodies  have,  in  city  water  systems,  caused  much 
trouble  by  clogging  the  fire  nozzles  or  water  pipes.  To  pre- 
vent the  throwing  out  of  such  masses  many  wells  have  been 
filled  with  lengths  of  perforated  pipe  dropped  to  the  bot- 
«.~™  „*  <-!,„  ,™n  '  lengths  of  pipe  thus  inserted  are  per- 
forated with  J£  or  %  inch  holes 
which,  while  admitting  the  water 
or  sand,  prevent  the  admission  of 
the  larger  solid  bodies.  The  conse- 
quence  of  thus  shutting  off  free 
access  to  the  well  is  that  large  quan- 
tities of  loose  rock  accumulate 
about  the  base  of  the  pipe,  as  shown 
in  Fig.  5,  thus  gradually  shutting  off 
:  the  water  supply  and  diminishing 
:  the  volume  and  efficiency  of  the 
well;  besides  which,  the  effective 
erea  of  the  base  of  the  well  pipe  is 
reduced  by  the  insertion  of  this 
smaller  pipe  thereby  still  further 
decreasing  the  capacity  of  the  well. 
Additional  disadvantages  of  this 
Fi  5  inserted  pipe  lie  in  the  fact  that  it 

Showing  a  perforated  pipe  is  out  of  reach  and  control,  it  be- 
in  the  bottom  of  a  well,  comes  a  loose  and  independent  feat- 
ure of  the  well,  not  under  control  or  subject  to  needed  re- 
pairs, and  it  is  apt  to  become  out  of  line  with  the  main  pipe 
—if  not  entirely  disconnected  from  it— thus  forming  a  pos- 
sible and  unmanageable  obstruction  at  the  base  of  the  well. 
If  the  perforated  pipe  is  left  out,  the  well,  at  the  bottom, 
will  be  clean  and  free  to  receive  whatever  comes  to  it.  If 
rock  is  thrown,  care  for  it  at  the  sruface  where  it  may  be 
collected  and  disposed  of.  Put  in  a  settling  reservoir  to  re- 
ceive it,  or,  in  case  of  water  works,  where  the  pressure 
must  stand  in  the  pipes,  run  the  water  through  a  large  sand 
drum  which  will  collect  the  heavy  matter  and  permit  only 
the  water  and  lighter  sediment  to  pass  to  the  mains. 

It  is,  indeed,  safer  to  collect  the  rock  at  the  surface,  where 
it  may  be  cared  for,  than  to  permit  it  to  accumulate  at  the 
base  of  the  pipe  where  it  cannot  be  cared  for  and  may  ruin 
the  well. 

If  the  well  becomes  stopped  up  by  an  accumulation  of 
sand  or  by  other  causes  the  pipe  may  be  more  easily  cleaned 
put  if  it  has  a  uniform  diameter  from  top  to  bottom  and  it 
is  unobstructed  by  the  presence  of  a  section  of  loose  perfor- 
ated pipe.  Usualiy  the  services  of  a  well  driller  will  be 
needed  to  open  up  a  well  which  has  become  clogged.  The 
objections  urged  against  the  use  of  perforated  pipe  in  wells 
are  not  founded  on  theory  alone  but  upon  actual  experience 


29  (A.  ^ 

in  a  number  of  the  more  important  Sy  ells  of  the  state. 
VALVES,  HYDRANTS  AND  SPECIADS^See  Fig  3  p  21) 

Every  well  should  have  at  le  ist  one  gate  valve  in  order 
that  it  may  be  shut  off  in  whole  or  in  part,  for  otherwise  no 
control  could  be  exercised  over  the  flow  by  the  person  in 
charge. 

The  kind  of  valve  to  buy  is  a  matter  of  importance,  for 
all  are  not  equally  good,  either  as  to  pattern,  workmanship, 
or  material.  Of  the  many  makes  of  valves  the  Ludlow  and 
the  Chapman  are  among  the  best  and  are  the  most  used  in 
the  Dakotas.  (See  adv't  Chapman  Valve  Co.,  P,  210;  of  the 
Ludlow  Valve  Co.  P.  224;  of  the  National  Tube  Works  Co. 
front  cover;  of  the  Brass  &  Iron  Works  Co.  P.  225;  and  of 
Kobinson  &  Cary  Co.  P.  242.) 

The  greatest  care  is  necessary  in  the  selection  of  a  hydiant 
for  water  works  service.  Almost  any  hydrant  will  work 
well  in  clear  water  but  few,  however,  will  prove  satisfactory 
in  case  sand  or  gravel  is  held  in  suspension  by  the  water. 
A  hydrant  haying  a  rubber  or  leather  face  or  cone  will  need 
frequent  repairs,  owing  to  pieces  of  sand  or  gravel  becom- 
ing imbedded  in  the  soft  surface.  These,  too,  tend  to  wear 
the  surface  of  the  metal  ring,  and  thus  leaks  are  caused  and 
the  hydrant  frequently  freezes  and  becomes  unserviceable. 

Where  there  is  much  grit  in  the  water  a  metal  faced  hy- 
drant should  be  selected.  Where  the  water  is  clear  the 
others  will  prove  as  good.  A  gate  valve  should,  be  handled 
carefully.  Do  not  close  it  suddenly  for  the  "Water  Ham- 
mer," due  to  the  sudden  checking  of  the  velocity  of  a  rapid- 
ly moving  column  of  water,  under  heavy  pressure,  is  very 
great  and  tends  to  injure  the  pipe  and  its  connections. 

The  arrangement  of  the  valve,  or  valves,  will  depend  upon 
the  circumstances  surrounding  the  well  and  its  uses. 

Usually  the  main  valve  is  placed  horizontally  on  the  main 
pipe  and  all  connections  are  made  above  the  valve.  In  this 
position  the  valve  is  usually  put  on  before  the  main  flow  of 
water  is  struck,  the  drilling  being  continued  through  the 
opened  gate— care  being  taken  to  protect  the  face  plates  of 
the  valves  by  a  thin  nipple  set  into  the  top  of  the  well.  If 
the  valve  is  not  set  until  after  the  flow  is  struck  much  loss 
of  time  and  money  may  result  before  it  is  finally  set  to  the 
pipe  against  the  force  of  the  flow.  (A  notable  instance  of 
this  was  that  of  the  first  "city  well,"  at  Aberdeen,  where  it 
was  found  to  be  impossible  to  set  the  valve  because  of  the 
force  of  the  water,  and  hundreds  of  dollars  were  wasted,  and 
special  tools  finally  constructed,  before  the  water  was  finally 
shut  off  and  the  valve  set.) 

This  danger  may  not  be  ever  present,  especially  in  the 
smaller  wells,  but  reference  to  it  will  call  attention  to  its 
consideration.  Sometimes  a  cross  is  set  first,  on  top  of 
the  pipe,  before  the  flow  is  struck.  It  is  then  an  easy  mat- 
ter to  set  the  gate  to  the  top  or  the  side  opening,  the  stream 
finding  a  partial  outlet,  meanwhile,  through  the  other  open- 


30 

ing.  After  the  gate  is  set  the  other  openings  may  be  plug- 
ged or  otherwise  connected. 

If  the  main  gate— or  any  gate  valve— is  set  on  any  line  of 
horizontal  pipe,  leading  from  a  well  throwing  any  sand  or 
solid  matter,  the  valve  should  be  set  vertically,  that  is,  with 
the  hand-wheel  at  the  top.  This  will  prevent  sand  or  stone 
lodging  in  the  working  parts  of  the  valve;  a  danger  which  is 
ever  present  if  the  hand-wheel  is  at  the  side  of,  or  under- 
neath, the  pipe. 

Whatever  may  be  the  location  of  the  valves,  or  the  use  to 
which  the  well  may  be  put,  one  thing  should  be  observed, 
which  is,  so  arrange  the  specials  (which  is  understood  to 
mean  the  crosses,  tees,  valves  and  such  similar  features  of 
the  pipe  fittings)  as  to  leave  a  vertical  opening  above  the 
main  pipe,  which  opening  may  be  closed  by  a  plug  if  not 
otherwise  connected. 

By  so  doing  ready  access  to  the  well  is  always  possible, 
for  the  purpose  of  cleaning  out,  blowing  off,  or  other  pur- 
pose, without  disturbing  the  other  connections  of  the  well. 

If  the  well  is  to  be  used  for  power,  in  the  running  of  a 
mill  or  other  heavy  plant,  much  power  may  be  saved  by 
using  long  curved  specials  instead  of  the  short,  right-angled 
specials  commonly  used.  Every  well  driller  ought  to  have, 
as  a  part  of  his  outfit,  a  full  set  of  specials  (crosses,  tees,  ys, 
nipples,  bushing,  plugs,  elbows  and  a  pressure  guage)  so 
that,  on  the  completion  of  a  well,  a  sufficient  test  of  its  pow- 
er and  volume  could  be  made  to  be  of  value  as  a  matter  of 
public  record  and  also  as  a  matter  of  value  to  the  driller 
himself,  who  would,  through  the  wide  publicity  given  to  all 
such  systematic  tests,  derive  a  direct  benefit,  in  the  way  of 
advertising  sufficient  to  pay  him  for  the  expense  and  time 
invested. 

The  more  such  matters  are  observed  the  more  will  public 
attention  be  called  to  our  artesian  wells  and  the  more  quick- 
ly will  capital  be  attracted.  Properly  viewed,  it  would  be  a 
wise  stroke  of  business  policy  for  every  well  owner  and  con- 
tractor to  interest  himself  in  these  features  of  a  well  and  to 
be  prepared  to  put  them  to  efficient  tests. 

Even  the  well  owner  cannot  afford  to  be  without  the  few 
specials  necessary  to  a  proper  control  over  his  well,  or  to  its 
direction  in  such  manner  as  may  best  suit  his  varied  needs. 
Supposing  the  well  to  be  6  inches,  what  ought  to  be  provided? 

1 — 6-inch  cross. 

1— 6-inch  tee. 

1 — 6-inch  elbow. 

2— 6-inch  plugs  (one  plugged  for  attachment  of  gauge.) 

2— 6-inch  nipples. 

2— 4-inch      " 

2— 2-inch      " 

1  nest  of  bushing  for  4-inch  and  2-inch  connections. 

1  pressure  gauge. 

With  these  few  specials  the  well,  or  any  connection  with 


31 

it  may  be  reduced  or  directed  as  occasion  may  require.    At 

least  these  specials  should  be  obtained. 

LOCATION  OF  WELL. 
As  a  rule,  a  well  for  irrigation  will  be  located  on  or  near 

the  highest  point  of  land  to  be  irrigated,  but  considerations 

of  convenience  or  economy  may,  at  times,  suggest  a  location 
at  a  lower  point  or  near  one's  buildings  from  which  location 
the  water  may  be  piped  to  the  higher  ground. 

The  reservoir  will  usually  occupy  the  highest  ground  and 
the  well  may  be  placed  at  the  most  accessible  point  near  it 
or  at  such  a  point  as  will  best  conserve  the  proper  division 
of  the  fields  or  the  location  of  the  ditches.  All  of  these 
things  should  be  considered  and  mapped  out  before  either 
the  well  or  the  reservoir  is  located;  otherwise  the  location 
may,  in  the  end,  prove  to  have  been  badly  chosen. 

At  whatever  point  the  well  is  located  let  that  point  be 
OUTSIDE  OF  THE  RESERVOIR,  Some  wells  have  been 
located  within  the  reservoir  where  they  are  not  accessible 
because  of  either  water  or  mud,  where,  in  case  of  needed  re- 
pairs, it  would  be  difficult  to  convey  the  machinery  and  sup- 
plies, or  to  erect  or  handle  the  same,  where  the  well  cannot 
conveniently  be  used  for  anything  else  but  to  supply  irri- 
gation waters  and  where  its  flow  could  not  be  easily  regu- 
lated during  the  winter  months. 

If  located  outside  of  the  reservoir  the  well  would  be  ac- 
cessible at  all  times  and  subject  to  control;  it  could  be  easily 
repaired  or  opened  up— if  stopped  up;— its  volume  could  be 
first  used  as  power  to  run  machinery,  a  revenue,  possibly, 
being  derived  from  the  rental  of  the  power,  and  the  water 
then  conveyed  to  the  reservoir  by  a  short  pipe.  It  could  be 
enclosed  and  protected  from  the  weather  as  every  well 
should  be  in  order  to  protect  and  preserve  the  pipe  and 
valves  from  rust,  for  the  well  is  but  a  piece  of  machinery 
and  should  be  cared  for  as  such.  It  will  wear  out  in  time  by 
rust  and  wear  and  will  need  recasing,  but  in  order  to  pre- 
serve it  as  long  as  possible,  its  pipes  should  be  painted  and 
protected.  If  thus  cared  for  it  will  last  intact  for  mapy 
years  and  pay  for  itself  many  times.  The  cost  for  repairs 
being  almost  nothing. 
LOG  OF  WELL. 

Section  35  of  the  "Melville"  law  provides  that  the  con- 
tractor of  any  township  well  shall  keep  a  log  of  the  well,  or, 
in  other  words,  a  record  of  the  successive  strata  through 
which  the  drill  passes.  From  the  very  nature  of  the  case 
this  must  be  a  dead-letter,  for  it  cannot  be  enforced. 

The  driller  may  report  such  a  log  as  he  chooses,  and  no 
one  else  be  the  wiser.  The  truth  is,  it  is  safe  to  say,  that  no 
properly  recorded  log  has  ever  been  made  of  a  Dakota  well. 
The  author  has  seen  many  wells  drilled,  and  has  carefully 
noted  the  methods  adopted,  but  in  only  one  case,  within  his 
knowledge,  was  there  any  effort  made  to  obtain  an  accurate 
log. 


32 

Dozens  of  records  have  been  published  in  papers  pam- 
phlets and  reports,  but  all  are  subject  to  grave  doubt,  as  to 
truth  or  accuracy.  Some  drillers  will  make  no  report— pre- 
fering  to  keep,  as  a  trade  secret,  whatever  they  may  have 
discovered — but  most  drillers  pay  no  attention  to  the  drill- 
ings, and,  except  for  the  fact  that  at  one  depth  the  drilling 
is  hard  and  slow,  and  at  another  depth  it  is  softer  and  more 
rapid,  they  know  little  or  nothing  about  the  character  of  the 
formations  in  which  they  have  worked. 

The  keeping  of  a  log  involves  considerable  extra  labor, 
systematic  watchfulness,  a  certain  degree  of  knowledge  of 
geology,  and,  above  all,  a  certain  amount  of  expense  to 
which  the  contracting  driller  does  not  care  to  go.  He  agrees 
to  drill  a  well,  and  not  to  instruct  in  geology,  and,  to  him, 
the  drillings  discharged  are  all  the  same. 

It  must  be  admitted  that  a  carefully  kept  log,  or  rather 
series  of  logs,  would  be  of  much  value,  but  how  to  secure 
them  is  a  question  each  driller  alone  can  decide.  Certainly 
section  35,  above  referred  to,  can  result  in  nothing  more 
than  a  succession  of  false  reports  which  will  be  worse  than 
none  at  all.  When  the  first  well  in  the  state  was  drilled, 
(the  Ry.  well  at  Aberdeen)  by  Mr.  Swan,  the  author  was 
present  daily  and  assisted  in  keeping  the  log,  preserved  sam- 
ples of  the  drillings,  dried  and  arranged  them,  and  finally 
mounted  them  in  3-foot  glass  tubes  secured  for  the  purpose. 

If  equal  care  was  used  with  each  well  the  logs  would  then 
approach  the  truth  and  possess  some  value.  Each  owner  of 
a  well  should  look  to  it  that  this  is  done. 

Equally  important— yes,  far  more  important— is  the  keep- 
ing of  an  accurate  record  of  the  performance  of  each  well, 
and  as  to  all  its  dimensions,  thus— depth  and  log,  and  length 
of  each  size  ot  casing  in  well.  Size  at  top  or  bottom,  or  all 
the  way. 

Pressure— When  closed,  and  when  flowing  from  openings  of  different 
sizes. 

Volume— When  open  full  and  when  throwing  streams  of  different  sizes ; 
not  guessed  at  but  carefully  measured  with  a  weir. 

Discharge— Exact  height  of  stream  thrown  vertically  when  well  is  opened 
full,  and  from  openings  of  1,  2,  3,  4.  6  or  8  inches.  Also,  the  ex- 
act distance  these  streams  will  be  thrown  horizontally, 

Temperature  of  the  water. 

Whether  hard  or  soft,  clear  or  sandy  or  muddy. 

The  exact  time  occupied  in  drilling  the  well,  with  dates. 

The  quality  of  pipe  used. 

The  kind  of  machine  used  in  drilling. 

The  exact  cost. 

There  is  nothing  in  the  above  form  of  record  that  cannot 
be  kept  by  any  farmer  or  driller  and  nothing  that  is  not  of 
importance  or  that  cannot  be  determined  if  only  a  few  spec- 
ials are  at  hand.  The  measurements  of  volume  and  height 
of  streams  are  simple  operations  and  are  fully  explained 
herein.  (See  measurements  by  weirs.)  See — how  to  meas- 
ure the  height  of  a  stream,  page  93.) 


33 

A  series  of  records  kept  as  above  suggested  would  have 
value,  but  the  records  as  heretofore  kept  have  but  little. 
Even  the  published,  official  records,  or  reports,  are  far  from 
accurate.  A  record,  once  carefully  made,  ought  to  be  pre- 
served for  future  reference,  for  the  memory  alone  cannot  be 
relied  upon. 
DEILLING. 

Little  need  be  said  under  this  head  for  it  is  assumed  that 
an  expert  will  be  in  charge  of  the  work.  If  an  inexperi- 
enced hand  is  in  charge  he  has  more  to  learn  than  a  book  of 
this  size  would  hold.  A  few  suggestions,  however,  will  be 
in  order. 

Do  every  part  of  the  work  thoroughly  and  with  the  greatest 
care.    Tjse  great  care  in  handling  tools  about  the  pipe 
so  as  not  to  drop  them  in. 
Make  every  joint  of  the  rod  or  the  tools  fast  so  they  will 

not  loosen,  and  cause  the  loss  of  a  rod  or  tool. 
Keep  the  drills  and  reamers  in  proper  cutting  order,  and 
inspect  everything  frequently  to  see  that  nothing  is  loose 
or  defective. 

Do  not  work  the  drilling  tools  too  long  before  pulling  out, 

for  it  is  better  to  pull  out  more  frequently,  and  make  sure 

that  everything  is  safe  and  sound,  than  to  attempt  to  work 

longer  and  lose  a  tool  by  reason  of  a  loose  joint. 

Above  all,  do  the  reaming  well,  so  that  the  pipe  will  settle 

easily  and  not  stick  or  require  heavy  driving. 
Keep  the  pipe  pretty  clos>e  to  the  bottom,  in  order  to  avoid 
the  caving  in  of  the  walls  or  the  inrush  of  quick  sands 
and  the  possible  sticking  of  the  tools.  Many  drillers  will 
run  from  20  to  100  feet  without  settling  the  pipe,  and  they 
usually  have  trouble  in  consequence.  Only  room  enough 
is  needed  below  the  pipe  to  work  the  drill  and  the  reamer 
and  usually  the  length  of  a  single  section  of  pipe  will  be 
ample. 

Do  not  sink  a  smaller  hole  below  the  main  hole,  for  it  may 
endanger  the  latter  work  by  causing  the  drill  to  stick  or 
drill  a  sloping  hole  into  which  the  pipe  cannot  be  forced. 
Never  leave  a  tool  standing  in  the  well,  for  a  cave-in  may 
bury  it  and  render  its  extrication  difficult  if  not  im- 
possible 

If  any  accident  happens  do  not  cease  labor  until  it  is  reme- 
died or  until  its  remedy  is  seen  to  be  impossible. 
Arrange  in  advance  for  all  supplies,  in  order  that  no  delay 
may   endanger  the  continuation  of  the  work.     A  "shut 
down"  often  sets  the  work  back  more,  and  causes  greater 
expense,  than  though  no  work  had  been  done. 
Always  leave  the  work  in  a  safe  condition  and  protected 
from  the  depredations  of  the  curious  and  thoughtless  on- 
lookers. 

Cautions  might  thus  be  indefinitely  extended— each  found- 
ed on  some  costly  experience  of  the  past— but  enough  has 
been  suggested  to  show  the  necessity  of  an  exercise  of  such 


34 

a  degree  of  care  and  watchfulness  as  is  required  in  but 
few  other  callings.    If  no  accident  happens  the  driller  de- 
serves  much  praise.    If  one  does  happen  he  usually  has 
himself  to  blame. 
COST  OF  WELLS. 

Many  thoughtless  enthusiasts  have  raised  the  cry  that 
wells  ought  to  be  drilled  for  from  $1,200  to  $2,000  but  such 
persons  are  not  authorities  and  do  not  know  whereof 
they  speak.  The  cost  of  a  well  depends  not  upon  one  thing, 
but  upon  many  things.  The  size  is,  of  course,  the  chief 
factor  for  the  pipe  for  a  large  well  will  cost  more  than  that 
for  a  small  well;  the  rig  used  must,  as  a  rule,  be  heavier; 
the  tools  heavier;  the  coal  and  water  used  will  be  much 
more;  and  the  labor  bill  will  be  much  greater  because  the 
drilling  will  take  longer.  The  location  of  the  well  will 
effect  its  cost.  If  within  the  limits  of  a  town,  having  a 
system  of  water  works  so  that  the  water  used  in  drilling 
may  be  readily  secured  (and  under  pressure),  the  otherwise 
large  water-hauling  bill  will  be  saved.  If  the  well  is  on  a 
farm,  or  where  no  water  is  at  hand,  the  hauling  bill  will 
mount  to  most  respectable  proportions. 

Add  to  these  items  the  cost  of  moving  the  rig  to  its  site, 
setting  it  up  and  taking  it  down,  hauling  the  pipe  and  fuel, 
to  say  nothing  of  the  many  certain  yet  unforseen  incidental 
expenses  and  you  have  the  well  driller's  bill  of  expense, 
minus  the  ever-present  chance  of  an  accident  which  may 
cost  hundreds  of  dollars  or  result  even  in  his  financial  ruin. 
No  man  of  good  business  judgment  will  assume  these 
risks  for  the  mere  chance  of  earning  dav's  wages.  He 
claims,  and  is  fairly  entitled  to  receive,  a  generous  compen- 
sation for  the  risk  he  assumes,  and,  in  addition  to  that,  such 
wages  as  his  skill  as  a  driller  entitles  him  to  receive. 

For  the  purpose  of  illustration  the  following  approximate 
cost  is  given  of  a  6  inch  farm  well  1,000  feet  deep: 

1000  feet  of  6  inch  pipe  @  .62  per  foot $  620 

Frieght— at  reduced  rates about  50 

Hauling  pipe  to  the  ground '• 

"       casing  pipe  away , " 

"       and  transporting  rig "  50 

Setting  up  rig "  150 

Taking  down  rig,  and  breakage "  100 

Fuel,  and  hauling  same " 

Hauling  or  obtaining  water '•  100 

Wear  and  tear  on  rig  and  tools 200 

One  gate  valve 30 

Couplings "  40 

Interest  on  investment  for  90  days  "  75 

Labor  bills  @  $10  per  day  for  60  days 600 

Total  "          $2,315 

In  this  estimate  it  is  assumed  that  but  60  days  are  con- 
sumed in  the  work  of  moving,  setting  up,  drilling  and  taking 


35 

down;  that  there  are  no  accidents  or  unusual  expenses  and 
no  delays. 

The  incidental  expenses  could  not  safely  be  figured  at  less 
than  $300,  and  most  of  the  other  items  given  are  figured  too 
law;  so  that,  without  any  allowance  for  incidentals,  accidents 
or  profit,  and  allowing  but  three  men  on  the  work,  and  but 
60  days  of  time,  the  expense  still  exceeds  $2300  for  a  6-inch 
well.  It  is  not  the  intention  to  throw  any  unfavorable 
light  on  the  matter  of  cost  of  wells,  but  rather  to  throw  on 
the  true  light,  and,  by  calling  attention  to  the  details,  dispel 
some  false  light. 

A  well  is  worth  all  it  costs, 

and  the  driller  must  have  some  show  as  well  as  the  owner. 
A  6-inch  well  costing  from  $3000  to  $4000  is  cheap,  if  prop- 
erly put  down,  and  is  a  grand  investment,  and  one  which  is 
better,  at  that  price,  for  the  farmer  than  for  the  driller,  for 
where  the  driller  may  make  $500  or  $1000  profit  on  one  well 
he  may  lose  it  all  on  the  next;  whereas,  the  farmer  with  the 
well  has  a  sure  thing  and  a  competency. 

Any  well  will  pay  its  cost  in  5  years— whatever  the  cost 
may  be— or  at  the  rate  of  20  per  cent,  on  the  investment. 
Some  wells  have  paid  for  themselves  in  one  year. 

If  a  farmer  has  a  well  which  enables  him  to  raise  even  30 
bushels  of  wheat  to  the  acre,  in  a  dry  year  when  his  neigh- 
bors fail  to  get  back  their  seed,  and  he  has  but  140  acres  un- 
der water,  he  receives  4,200  bushels,  which,  at  but  50  cents 
per  bushel,  nets  him  $2,100,  or  sufficient  to  pay  for  a  well 
large  enough  to  thoroughly  irrigate  his  160  acres.  This  is 
not  overdrawn  but  underdrawn  as  based  upon  actual  expe- 
riences. One  well,  in  1891,  more  than  paid  its  cost  by  garden 
irrigation,  and,  besides  this,  supplied  water  to  the  town. 

Many  such  examples  could  be  given  to  show  how  service- 
able a  well  is  and  how  short  a  time  it  takes  to  return  its 
cost.  Nor  need  one  seek  a  dry  year  in  order  to  show  the 
contrast,  for  even  in  the  best  years  the  service  of  a  well  is 
so  great  as  to  make  the  increased  yield  pay  very  largely  on  its 
cost. 

It  may  be  asked— what  do  your  Dakota  wells  cost  ?  The 
answer  would  be  difficult  to  frame  for  lack  of  proper  infor- 
mation and  knowledge  of  all  the  facts  entering  into  the 
matter  of  cost.  Wells  4jor  4J^  inches  have  cost  from  $1,800 
to  $3,000.  Wells  of  6  inches  from  $3,000  to  $7,000;  although 
about  $3,000  is  the  common  price.  Wells  of  8  inches  have 
cost  about  $4,000  or  So, 000.  The  expensive  wells  have,  in 
all  cases,  been  expensive  by  reason  of  delays  and  accidents. 
As  drillers  have  become  more  skilled  in  this  field,  and  rigs 
have  been  adapted  to  its  formations,  the  price  of  wells  has 
been  reduced,  and  a  still  further  reduction  may  be  expected 
as  skill  and  competition  increase.  The  cost  of  a  Dakota 
well  ought  to  be  considered  in  connection  with  its  volume. 
The  mere  hole  has  no  value;  it  is  the  water  which  it  supplies 
on  which  a  value  is  placed. 


36 

The  hole  costs  so  much,  regardless  of  the  volume  of  water 
thrown  out,  so  that  if  two  wells  cost  $2000  each,  and  one 
well  throws  out  1000  gallons  per  minute,  while  the  other 
throws  out  but  500  gallons  per  minute,  it  may  be  fairly  said 
that  one  well  cost  twice  as  much  as  the  other,  for  the  one 
supplies  but  half  the  service  of  the  other,  or  has  cost  twice 
as  much  for  a  given  return.  80,  too,  as  between  Dakota 
wells  and  those  of  other  sections  of  the  country. 

The  Dakota  artesian  basin  is  the  largest  and  the  greatest 
in  the  world  and  the  volumes  and  pressures  of  its  wells 
greater  than  the  volumes  and  pressures  elsewhere.  So  it 
may  be  said  that  it  costs  far  less  here  to  get  a  given  volume 
of  water  than  it  does  any  where  else  in  the  world.  This  ba- 
sin is  the  nearest  to  the  manufacturers  of  well  machinery, 
pipe,  tools,  and  other  supplies  which  therefore  cost  less. 
The  depths  are  but  moderate,  and  the  volumes  enormous,  so 
that  the  duty  or  service  received  for  the  money  expended  is 
greater  than  in  any  other  section  or  country. 

In  Australia  many  wells  are  put  down  by  the  government 
at  a  cost  of  from  $5,000  to  $25,000,  yet  their  best  wells  do 
not  equal  the  average  Dakota  wells.  Our  farmers  may 
therefore  deem  themselves  most  highly  favored  by  nature 
and  ought  not  to  grumble  at  the  expense  of  obtaining  water, 
for,  by  no  other  system,  and  in  no  other  section  of  the 
world,  can  an  equal  volume  be  obtained  for  the  same 
amount  of  money.  No  reasonable  man  will  complain  of  ex- 
pense when  he  pays  far  less  than  the  balance  of  mankind 
and  when  all  the  conditions  are  so  favorable  for  the  speedy 
return  of  the  money  invested. 

Nor  will  any  wise  investor  hesitate  to  put  his  money  into 
Dakota  wells  or  farm  lands  when  the  conditions,  as  they  are 
here,  are  shown  to  him  in  comparison  with  the  conditions 
elsewhere,  under  which  conditions  tens  of  millions  have 
been  invested  to  the  great  profit  of  the  investor,  prosperity 
of  the  settler,  and  glory  of  the  state  and  nation. 

It  must  further  be  considered  that  the  cost  of  the  water 
is  but  a  part  of  the  cost  of  the  land.  The  well  is  of  no  val- 
ue except  as  it  supplies  the  water;  the  water  is  of  little  val- 
ue except  as  it  feeds  the  ground  and  aids  in  producing  a 
crop.  The  cost  of  land,  well,  ditches,  reservoirs  and 
other  improvements  could  properly  be  "lumped,"  and  the 
total  value  per  acre  found.  In  this,  as  in  the  cost  of  the 
water  alone,  Dakota  will  be  shown  to  hold  the  palm  as 
against  the  world.  This  matter  will  be  more  fully  consider- 
ed under  the  head  of  land  and  water  values. 

Some  have  asked— how  can  I  get  a  well  the  cheapest  ?— by 
contracting  with  a  driller,  or  by  buying  a  rig  (either  alone 
or  by  clubbing  together  with  my  neighbors)  and  doing  my 
own  work.  Many  reasons  prevent  a  reply.  Firstly,  iusffici- 
ent  data  as  to  what  has  been  done  heretofore  renders  a  reply 
impossible,  or,  at  best,  purely  speculative.  Secondly,  the 
outcome  will  depend  upon  who  you  are,  what  your  means 


37 

may  be,  what  your  general  intelligence  may  be,  and  espec- 
ially as  to  the  amount  of  natural  mechanical  ability  you 
may  possess.  Many  farmers  could  not  drill  a  well  with  the 
best  of  tools.  Some  ingenuous  farmers  have  actually  drilled 
good  wells  with  rigs  and  tools  of  their  own  make.  Safety 
and  economy  would  appear  to  lie  in  the  selection  of  a  con- 
tractor who  has  the  tools,  knows  the  business  and  is  prepar- 
ed to  assume  all  risks.  It  is  to  be  hoped,  however,  that 
hundreds  of  rigs  will  be  purchased  by  farmers,  and  that  we 
may  soon  evolve  a  race  of  practical  drillers  from  among  our 
own  people. 
AETESIAN  WELLS,  ELSEWHERE. 

It  is  within  a  comparatively  short  time  that  artesian  well 
waters  have  been  used  for  irrigation  in  this  country,  but 
their  value  is  now  being  appreciated  and  thousands  are  be- 
ing sunk  for  this  purpose.  As  above  stated,  there  has  not 
yet  been  discovered  in  the  world  another  artesian  basin  of 
such  extent  as  the  Dakota  basin  nor  one  whose  wells  possess 
such  great  volume  and  pressure. 

Artesian  wells  are  common  to  nearly  all  of  our  states  and 
to  most  countries  and  some  few  wells  have  been  drilled 
that  compare  very  favorably  with  the  better  Dakota  wells 
but  they  are  few  in  number  and  widely  separated,  and  the 
artesian  basins  thus  far  discovered  are  of  but  moderate 
area.  The  Dakota  sand-rock  formations  extend  far  to  the 
south  so  that  Nebraska  and  Kansas  have  a  few  good  wells 
but  most  of  the  southern  wells  are  shallow  and  the  flow  but 
weak . 

A  group  of  5  wells  at  Coolidge,  Kansas,  cost  an  average  of 
8400  each  and  have  an  average  flow  of  25  gallons  per  min- 
ute. A  like  ratio  between  cost  and  volume  would  make  a 
Dakota  well  of  1800  gallons  cost  $16.000,  whereas  there  are 
several  throwing  a  greater  volume  the  cost  of  which  has 
been  from  $3,000  to  $4,000.  The  smaller  wells  of  the  Crook- 
ed Creek  Valley,  numbering  about  100,  and  costing  only 
about  $20  each  are  used  for  irrigation  and  about  50  of  these 
serve  from  5  to  25  acres  each. 

A  new  artesian  basin  has  but  recently  been  discovered  in 
Washington,  in  the  Yakima  valley,  where  there  is  one  well 
flowing  650,000  per  day  or  452  gallons  per  minute.  This 
would  rank  among  the  smaller  wells  of  Dakota.  A  com- 
pany has  been  organized  to  drill  wells  throughout  this  new 
field  wherein  hundreds  of  thousands  of  dollars  have  been 
expended  in  irrigation  development  by  other  systems  and 
where,  within  a  decade,  a  barren,  sage-brush  desert  has  been 
made  the  home  of  the  peach  and  the  prune,  and  the  heart  of 
a  vast  and  prosperous  agricultural  interest. 

In  Colorado  several  thousand  wells  have  been  drilled  to 
depths  ranging  from  100  to  1800  feet,  but  in  most  cases  to 
depths  of  from  300  to  700  feet .  The  water  from  many  must 
be  pumped  but  in  most  other  cases  the  flow  ranges  from  10 
to  75  gallons  per  minute. 


38 

The  town  well  at  Anamosa  has  a  liow  of  495  gallons  per 
minute.  This  is  the  largest  of  over  2000  wells  in  the  San 
Louis  valley,  Bucher's  well,  at  the  same  place  has  a  pres- 
sure of  25  pounds  to  the  square  inch.  The  Espinosa  well, 
about  20  miles  north  of  Monte  Vista,  according  to  the  re- 
port of  the  state  engineer,  u  throws  a  solid  three-inch  col- 
umn of  water  nearly  40  inches  above  the  casing,  and  flows 
between  300  and  400  gallons  per  minute." 

Compare  this  pigmy,  which  thus  deserves  special  notice 
in  Colorado,  with  such  Dakota  gushers  as  the  Aberdeen, 
Huron,  Kedfield,  Doland,  Columbia,  Woonsocket,  Spring- 
field and  Yankton  wells  not  to  mention  a  host  of  others 
each  of  which  would  be  a  marvel  in  any  other  land. 

In  California  there  are  25  artesian  basins  of  varying  char- 
acter and  pressure  but  that  of  Kern  county  is  the  most  re- 
markable and  more  nearly  resembles  the  Dakota  basin  than 
any  other  yet  found.  Its  area  is  only  about  18  by  14  miles 
and  it  has  an  elevation  of  about  300  feet  above  the  sea.  The 
average  depth  of  the  many  wells  in  this  area  is  about  500 
feet.  Ol  these  wells  54  range  in  flow  from  150,000  to 
4,000,000  gallons  per  day,  or  from  100  to  3,000  gallons  per 
minute. 

One  wells  has  a  volume  of  3,000  gallons  per  minute,  two 
wells  flow  2,100  and  2,400  gallons,  nine  wells  flow  from  1,400 
to  2,000  gallons,  and  seventeen  wells  flow  from  700  to  1,400 
gallons  per  minute.  The  diameters  range  from  6  to  10 
inches. 

The  counties  of  Tulare,  Los  Angeles  and  San  Bernardino 
have  also  remarkable  artesian  basins  and  hundreds  of  very 
fine  wells  from  150  to  500  feet  in  depth.  About  4  miles 
south  of  San  Bernardino  is  the  Gage  group  of  29  wells,  all 
within  the  radius  of  a  mile,  the  average  volume  being  about 
389  gallons  per  minute,  and  the  average  depth  but  150  feet. 

In  other  parts  of  the  United  States  there  are  many  nota- 
ble wells  and  artesian  basins,  as  there  are  also  in  China,  in 
the  Sahara  desert,  and  in  nearly  all  of  the  countries  of 
Europe,  especially  in  Germany  and  in  France.  The  scope 
of  this  little  book  will  not,  however,  permit  their  considera- 
tion. It  is  sufficient  to  note  that  the  artesian  well  is  of 
world- wride  interest  to  mankind  but  it  is  in  Dakota  that  the 
great  wells  may  be  saidto  be  at  home. 
DAKOTA  WELLS. 

The  pioneer  well  of  Dakota  was  begun  in  the  summer  of 
1881,  at  Aberdeen,  by  the  Chicago,  Milwaukee  &  St,  Paul 
Ry.,  for  the  purpose  of  supplying  water  for  its  engines. 
The  well  was  drilled  by  Mr.  Swan,  and,  by  reason  of  changes 
in  the  size  of  pipe,  and  unavoidable  delays,  the  cost  was  far 
greater  than  it  would  otherwise  have  been.  The  flow  was 
struck  early  in  the  spring  of  1882,  at  a  depth  of  920  feet, 
The  pipe  was  6  inches  at  the  top  and  4^  at  the  bottom. 
The  volume  was  not  accurately  measured  at  the  time  but 
a  very  close  approximate  measurement  placed  the  volume  at 


39 

1,200  gallons  per  minute  and  this  increased  later  on  to  over 
2,000.  The  pressure  ranged  from  150  to  180  pounds  to  the 
square  inch.  The  6  inch  pipe  was  carried  to  a  height  of  70 
feet  and,  from  a  2-inch  nozzle  at  the  top  of  this  pipe,  a 
stream  was  thrown  60  or  70  feet  into  the  air  against  a 
gentle  breeze.* 

Encouraged  by  the  success  at  Aberdeen,  other  wells  soon 
followed  throughout  the  length  of  the  territory  until,  today, 
they  stretch  over  an  area  of  over  400  miles  north  and  south 
by  over  a  hundred  miles  east  and  west,  and  the  limit  of  the 
field  in  any  direction  has  yet  to  be  found. 

A  complete  list  of  Dakota  wells  could  not  be  given  for 
lack  of  information,  but  a  list  is  given  below  of  a  few  typic- 
al wells  which  may  be  taken  not  as  exceptional  wells  select- 
ed for  the  purpose  of  parade  but  as  purely  representative 
of  the  wells  in  all  parts  of  the  state— such  wells  as  any 
farmer  in  the  state  can  get  if  he  will  but  try,  ajid  wells 
which,  when  once  obtained,  will  be  to  the  owners  a  mine  of 
wealth  such  as  few  at  present  dream  of. 

TABLE  NO.  13. 

KEPRESENTATIVE    SOUTH    DAKOTA 
WELLS. 


County. 

Town 
or 
Location. 

Depth 
in 
feet 

Bore 
in 
inches. 

Flow 
in  gals, 
per  min. 

Pressure 
in  Bbsper 
sq.  in. 

Aurora 

Plankinton 

.     750 

6 

1000 

Beadle 

Huron     well 

862 

5% 

1668 

120 

• 

Day" 

840 

4 

476 

120 

*'  Risdon" 

960 

5% 

2250 

175 

4 

Hitchcock 

960 

4&3 

1240 

155 

Brown 

Aberdeen,  Cy 

908 

5% 

1800 

180 

4 

•'     Sewer 

1000 

6-41/2 

1215 

155 

4 

"    Beard 

1050 

6&5 

1000 

138 

Columbia 

966 

41/2 

1399 

160 

Bon  Homme 

Springfield 

592. 

8 

3293 

80 

Tyndall 

735 

4H 

552 

45 

Douglas 

Armour 

725 

4H 

700 

Hand 

Miller 

1H5 

3y2 

462 

100 

Hughes 

Harrold 

1453 

150 

40 

Marshall 

Britton 

1004 

41/2 

601 

120 

Sanborn 

Woonsocket 

725 

5000 

153 

44 

44 

775 

7 

7000 

150 

Spink 

Ashton 

900 

4 

750 

100 

44 

Mellette 

910 

4H 

1215 

165 

Redfield 

964 

A 

1261 

166 

4< 

Doland 

897 

UA 

710 

112 

44 

Baker  well 

920 

44 

2000 

165 

Yankton 

Yankton 

610 

6 

1800 

56 

" 

*' 

610 

6 

2200 

50 

The  author  compiled  the  above  table  from  previously  published  re- 
ports and  has  made  such  corrections  as  were  possible.  The  figures  given, 
are,  in  the  main,  correct. 

*This  is  the  first  accurate  account  published  as  to  this  first 
well.  The  record  was  made  by  myself  at  the  time  and  has 
been  carefully  preserved.  The  record  published  by  State 


40 

Engineer  Coffin  was  erroneous,  having  been  obtained,  no 
doubt,  from  parties  who  were  not  properly  informed.  Sim- 
ilar errors  appeared  as  to  other  wells,  as  to  which  1  am  ac- 
curately posted.  The  official  reports  ought  to  be  as  accur- 
ate as  possible  and  none  but  the  best  authorities  accepted. 
It  is  difficult,  however,  to  attain  to  great  accuracy  in  this 
matter.  Maj.  Coffin  deserves  praise  for  attaining  so  nearly 
to  it.  __  W.  P.  B. 

The  Dakota  artesian  basin,  as  stated,  is  of  unknown  ex- 
tent. Wells  are  found  throughout  the  length  of  the  two 
Dakotas  and  far  northward  into  the  British  possessions,  as 
they  are  also  to  the  south  through  Nebraska,  Kansas  and 
Texas.  On  the  east  the  field  appears  to  terminate  within 
the  borders  of  the  state,  where  first  appear  the  quartzite  for- 
mations. Certain  evidences  are  adduced  by  Maj.  F.  F.  B. 
Coffin,  ex-state  engineer,  to  prove  that  even  \vithin  the 
quartzite  area  wells  may  be  found,  and  that  the  true  limit  on 
the  east  is  in  Minnesota  where  the  truearchaean  formations 
appear.  To  the  west  is  a  domain  as  unknown  as  it  is  vast. 
If  the  supply  of  this  basin,  as  supposed,  comes  from  the 
mountains  of  Wyoming  and  Montana,  then  it  would  be 
possible  to  find  wells  at  all  points  between  the  Missouri 
river  and  the  mountains  except  within  such  areas  as  have 
been  affected  by  igneous  upheavals  or  other  geologic  dis- 
turbances. 

It  is  sufficient,  however,  to  know  that  on  any  section  with- 
in this  broad  basin,  extending  for  over  400  miles  north  and 
south  by  about  100  miles  east  and  west,  a  well  may  certainly 
be  had.  The  water  bearing  formation  is  the  Dakota  sand- 
rock,  a  formation  of  unknown  thickness  in  this  field  al- 
though of  vast  thickness  in  its  far  western  out-croppings. 

The  southern  wells  of  the  state  penetrate  this  formation 
at  a  depth  of  about  600  feet.  The  formation  dips  thence  to 
the  northward  until,  at  Jamestown,  on  the  Northern  Pacific 
it  is  over  1400  feet  below  the  surface.  The  dip  appears  to 
be  comparatively  uniform  so  that  it  is  possible  to  determine, 
within  very  close  limits,  at  what  depth  water  will  be  struck 
at  any  point. 

Overlying  this  soft,  porous,  water-bearing  sand- rock  there 
is  usually  a  thin  stratum,  or  cap-rock,  of  harder  sandstone 
or  limestone.  Above  this  the  formations  are  principally  of 
blue  and  gray  shale  with  occasional  strata  of  sand  or  lime- 
stones. It  is  the  drilling  in  these  shale  formations  that  is 
so  difficult,  for,  as  stated  by  some  drillers,  the  shale  seems  to 
pack  like  putty  or  lead  and  does  not  mix  readily  with  the 
water  used  in  drilling. 

Much  has  yet  to  be  learned  as  to  Dakota  wells,  as  to  the 
formatioms  to  be  penetrated,  as  to  the  relationship— if  any 
there  be— between  volume  and  pressure  and  as  to  the  source 
and  the  volume  of  supply,  and,  especially  as  to  the  best  and 
cheapest  way  of  drilling  wells,  the  best  machinery  or  process 


41 

to  use  arid,  above  all,  the  best  use  to  be  made  of  the  water 
after  it  is  obtained.  The  Dakota  farmer  has  also  to  learn 
how  to  use  the  water  so  as  to  get  out  of  it  the  highest  duty, 
when  to  use  it  on  different  crops  and  in  what  quantity  on 
different  soils  and  durine:  different  seasons.  A  grand  work 
is  well  begun,  and  our  farmers  have  but  to  labor  and  gain 
dollars  thereby,  while  the  scientist  speculates  upon  the  mar- 
vels of  nature  as  they  develop  and  gains  knowledge  from 
his  speculations. 

Under  the  head  of  Water,  and  of  Reservoirs,  will  be  found 
several  tables  relating  to  the  duty  of  well  waters.  The  vol- 
umes of  wells,  yol nines  thrown  per  minute  and  per  day  and 
volumes  per  minute  equal  to  given  volumes  per  day,  vol- 
umes thrown  in  one  and  three  months  by  wells  of  different 
volumes  per  minute,  volumes  required  to  cover  different 
areas  to  different  depths  and  time  required  by  different 
wells  to  do  it,  equivalence  of  cubic  feet  and  gallons  and 
of  gallons  and  cubic  feet,  equivalence  of  other  units  of 
volume  or  measurement,  and  other  tables  of  value  relating 
to  wells. 

The  sequence  of  our  subject  requires  that  the  Water  fol- 
low the  completion  of  the  well,  so  that  "  Water,  its  pro- 
perties, measurement,"  tfec  will  next  be  briefly  considered; 
after  which  will  be  a  brief  consideration  of  the  matters  of 
storage  by  reservoirs  and  its  distribution  by  ditches,  flumes 
and  pipes. 

COPIES  OF  THIS  BOOK 

FOR  SALE   BY 


Aberdeen,  South  Dakota,  for  25  cents. 

Also  sets  of  detailed  drawings  of  gates,  outlets,  flumes, 
weirs,  and  similar  constructive  details  of  an  irrigation 
plant.  These  drawings  could  not  be  inserted  in  this  book. 
Price  per  set  25  cents . 


WATER. 

Its  Properties,  Duty  and  3ieasurement,  with  tables  of 

Weight,  Pressure,  Volume,  Discharges,  &c  &c. 

Miscellaneous  Notes. 

Pure  water  is  composed  of  Hydrogen  and  Oxygen. 

By  weight,  ll.l  88.9        Parts. 

By  measure ,  2  1  " 

Its  greatest  desity  is  at  a  temperature  of  from  39.2°  to 
39.8C  from  which  point  it  expands  by  either  heat  or  cold. 
It  boils  at  a  temperature  of  212  ,  and  freezes  at  32°  Fahr. 
Evaporates  at  all  temperatures. 


Is  but  slightly  compressible. 

Is  not  palatable  when  pure  or  distilled. 


Wieght— See  P.   62  &  63  Tables  of  weight,   and   notes 

appended. 

Weight— See  P.  61  "       "       "       on  one  acre. 

Pressure— See  P.  64  "       "       pressure. 

of  column  per  sq.  in.  =  height  of  column  X  4.331. 
"        "        "  "    circ.  in.  =  height  of  column  x  .3369. 

Press,  of  1  Ib  per  sq.  in.  is  exerted  by  column  2.311  ft.  high. 
Volumes— See  tables  under  head  of  Mensuration ,  and  fol- 
lowing tables. 

A  cu.  ft.  of  saturated  air  at  50°  contains  4.09  gr's.  of  water. 

A  cu.  ft.  of  saturated  air  at  55°  contains  4.86  gr's.  of  water. 

A  cu.  ft.  of  saturated  air  at  60°  contains  5.79  gr's.  of  water. 
A  fall  of  snow  of  11  inche^is  equal  to  about  one  inch  of 

rain,  but  this  varies  greatly.    11  inches  being  for  a  dry  snow 

not  drifted . 

Depth  of  water  in  in's.  X  2,323, 200= cu.  ft.  per  square  mile. 

Depth  of  water  in  inches  X 3,630=  cubic  ft.  per  acre. 

The  "CENTER  OF  PRESSURE"  is  %  of  the  depth  from 
the  surface-  Thus,  in  a  reservoir  or  tank  12  feet  deep  the 
average  pressure  on  the  sides  will  be  found  at  a  point  8 
feet  below  the  surface.  The  amount  of  this  pressure  is 
equal  to  the  depth  of  this  point  X  by  62%  (the  weight  of 
1  cu.  ft.  of  water).  In  this  case  8  ft.,  the  depth,  X  62%= 
499  pounds = the  average  pressure  per  sq.  ft.  on  the  entire 
surface .  To  get  the  total  pressure  on  the  sides  multiply 
the  total  area  of  the  sides  by  the  average  pressure,  as 
above  found.  The  total  pressure  on  sides  and  bottom  = 
3  times  the  weight  of  the  fluid  contained  in  the  tank  or 
reservoir. 

The  pressure  on  a  sluice  gate,  in  the  bank  of  a  reservoir, 
2x3  feet  and  the  center  8  feet  b  low  the  surface  of  the  wa- 
ter in  the  reservoir =8x62% =499  Bbs.  per  foot;  2x3=6  sq. 
ft.  X499=  2994  pounds,  or  nearly  1%  tons. 

The  daily  supply  of  water  per  capita  in  cities  having  water 
works  systems  ranges  from  45  to  175  gallons,  and  averages 
about  75  gallons.  In  nearly  all  cases  the  per  capita  de- 
mand increases  from  year  to  year. 

Water  presses  towards  an  orifice  from  all  directions  and 
diminishes  the  velocity  it  the  proportion  of  about  63  to 
100;  or  the  quantity  delivered  through  the  orifice  will  be 
less  in  this  proportion  than  the  calculated  amount. 


43 

DUTY  OF  WATER. 

By  the  duty  of  water  it  is  meant  the  amount  of  duty  or 
service  it  will  perform,  or  the  extent  of  its  usefulness  in 
any  given  field. 

Considered  as  a  power,  it  is  so  many  horse  power  for  a 
given  volume  under  a  given  head.  Considered  as  an  irri- 
gating medium  its  duty  is  the  number  of  acres  a  given  vol- 
ume will  adequately  serve;  or,  as  it  is  usually  stated,  the 
duty  of  a  second  foot  is  so  many  acres.  That  is  to  say,  a 
volume  of  one  cubic  foot  per  second,  fio\ying  constantly 
during  the  irrigation  season,  will  serve  a  given  number  of 
acres. 

This  element  of  duty  is  not,  of  course,  a  subject  of  exact 
measurement  for  too  many  variable  elements  enter  into  its 
determination  to  render  this  possible;  yet  the  duty  may,  in 
any  particular  section,  be  very  clearly  estimated.  What  the 
duty  will  be  will  depend  altogether  upon  the  crop  to  be 
served,  and  the  nature  of  the  sub-soil  and  surface  soil  on 
which  the  crop  is  grown. 

The  duty  in  one  state  will  differ  from  the  duty  in  another 
state,  as  will  the  duty  in  one  section  of  a  state  differ  greatly 
from  that  in  another  section  of  the  same  state.  One  crop 
will  require  more  water  than  another,  or  the  same  crop  may 
require  more  water  on  one  soil  than  on  another. 

In  Dakota  little  is  known  as  to  the  duty  of  water  for,  as 
yet,  no  measurements  have  been  made,  no  extended  system 
of  irrigation  is  in  practice  and  little  thought  has  yet  been 
given  to  this  matter;  nor  has  any  effort  been  made  to  arrive 
at  the  maximum  duty  of  any  one  well.  When  the  township 
well  system  becomes  general,  and  the  greatest  service,  or 
duty,  is  demanded  of  each  well,  then  will  carefully  kept  re- 
cords of  duty  be  required,  and  such  records  will  form  the 
basis  of  estimates  which  will  closely  approximate  to  the  duty 
of  the  well  waters  in  the  several  sections  of  the  state,  and 
lead  to  a  knowledge  of  better  methods  of  application  and 
conservation  of  the  supply. 

Noi  is  duty  a  constant  quality  for  it  is  constantly  on  the 
increase;  that  is,  the  duty  increases  from  year  to  year — oth- 
er things  being  equal— the  ratio  of  increase  being  very  rap- 
id immediately  after  the  installation  of  the  system  of  irri- 
gation This  is  apparent  on  considering  that  when  the 
water  is  first  applied  its  volume  is  very  largely  absorbed  in 
placing  the  soil  in  proper  condition.  This  having  been  done, 
the  same  volume  will,  the  next  year,  serve  to  supply  the 
prepared  area  and  still  leave  a  surplus  for  the  reclamation 
of  a  further  area. 

So,  each  year,  the  field  of  duty  is  extended  until  the  max- 
imum is  finally  reached.  As  stated,  the  duty  in  any  locality 
will  depend  very  largely  on  the  nature  of  the  soil,  and  it  will 
depend  still  more  upon  the  mean  rain  fall  over  that  section. 
In  a  locality,  or  during  a  year,  where  the  precipitation  is 
small  and  nearly  the  full  necessary  supply  must  be  artifici- 
ally supplied  the  duty  will  be  low;  but  where  the  precipita- 
tion is  nearly  sufficient  to  supply  the  needs  of  agriculture, 


44 

and  but  a  small  portion  need  be  artificially  supplied,  then 
the  duty  will  be  high. 

In  considering,  therfore.  what  the  probable  duty  in  Dako- 
ta will  be,  account  must  be  taken  of  the  character  of  the 
soil,  the  comparative  precipitation  and  evaporation  and  the 
nature  of  the  crop. 

Hon.  J.  S.  Greene,  state  engineer  of  Colorado,  in  the  1888 
report  states,  as  an  approximate  estimate,  that  the  precipi- 
tation on  the  mountain  areas  west  of  the  great  continental 
divide  is  33  inches,  and  on  the  plains  areas  10.7  inches;  an 
average  over  the  whole  of  that  area  of  25  inches.  Also  that 
on  the  mountain  areas  east  of  the  divide  the  precipitation 
is  30  inches,  and  on  the  plains  areas  15  inches;  or  a  total 
average  of  18.7  inches.  He  states  further,  and,  in  this,  is  in 
accord  with  other  authorities,  "  that  the  limit  of  remunera- 
tive farming,  without  irrigation  is  drawn  at  an  annual 
precipitation  of  twenty-two  inches"  that  is,  if  the  precipi- 
tation is  less  than  22  inches  there  cannot  be  certainty  as  to 
a  remunerative  return  for  agricultural  labor.  The  matter 
of  distribution  of  this  precipitation  enters  here  as  a  matter 
of  the  greatest  importance  as  shown  by  the  example  cited 
on  page  92. 

In  this  report  it  is  further  stated,  with  reference  to  the 
duty  of  water  and  the  distribution  of  precipitation— "as 
there  is  a  demand  for  general  results  in  this  matter,  it  may 
be  stated,  relative  to  the  duty  of  water  on  the  plains  of  Col- 
orado, measured  where  distributed  to  the  land,  that  one  sec- 
ond foot,  running  throughout  the  irrigation  season,  in  addi- 
tion to  about  5  inches  of  lam-fall  during  April  and  May, 
and  4.5  during  June,  July  and  August,  if  distributed  with 
fair  care  to  diversified  crops,  on  what  might  be  called  aver- 
age land,  would  irrigate  from  60  to  70  acres.  It  is  noticed 
that,  to  accomplish  this  duty,  it  must  be  measured  where 
placed  upon  the  land.  This  is  not  always  considered  when 
speaking  of  the  duty  of  of  water. "  (P.  406.) 

Referring  to  table  14,  below,  it  will  be  seen  that  the  pre- 
cipitation during  April  and  May,  in  Dakota,  has  equaled  or 
exceeded  5  inches  in  past  years,  except  daring  1890  and  1891; 
and  that,  in  every  year  the  precipitation  during  June.  July 
and  August  has  exceeded  5  inches,  so  that  the  conditions  of 
distribution  above  quoted  are  much  exceeded  here,  and 
hence  the  duty  of  our  well  waters  would  exceed  the  duty 
quoted  (soil,  average  evaporation,  and  average  humidity  be- 
ing  equal.) 


Year 

Pr.  Apl  &  May 

Pr.  June,  July  &  Aug 

Total 

.1882 

8.68 

13.18 

21.86 

1883 

6.59 

11.30 

17.89 

1884 

5.60 

9.47 

15.07 

1885 

6.26 

13.84 

20.10 

1886 

5.10 

9.12 

14.22 

1887 

5.11 

15.07 

20.18 

1888 

5.86 

7.67 

13.53 

1889 

6.45 

5.21 

11.66 

1890 

3.52  . 

8.01 

11.53 

1891 

3.89 

10.52 

14.41 

TABLE  NO.  14. 

Table  of  precipitation 
in  Dakota  during  Apl. 
and  May  and  during 
June,  July  and  Aug. 
(From  table  No.  43.) 


Averages      5.70 


10.34 


16.04 


45 

Then,  too,  the  average  Colorado  precipitation  of  18  or  19 
inches  is  less  than  the  Dakota  average  of  about  21  inches, 
so  this  operates  still  further  to  increase  the  probable  duty 
of  water  here. 

In  the  recently  published  report  of  State  Engineer  J.  P. 
Maxwell,  of  Colorado,  (1890  report)  are  certain  very  perti- 
nent suggestions  and  estimates,  relative  to  water  duty 
which  I  cannot  do  better  than  to  quote. 

"Water  rights  vested  on  the  basis  of  the  low  duty  assigned 
to  water  ten  years  ago,  have,  in  instances,  deteriorated  lands 
and  reduced  their  productiveness  by  as  urfeit  in  application, 
while  on  adjoining  lands  through  an  enforced  economy,  a 
higher  duty,  better  conditions  of  soil,  and  greater  produc- 
tiveness have  resulted." 

"  Unskilled  labor  has  a  penalty  of  25  to  50  per  cent  attach- 
ed to  it  in  the  application  of  water,  and  unfortunately  this 
class  is  too  prevalent  in  the  irrigation  fields,  in  many  cases, 
no  other  being  obtainable." 

"An  abundant  water  supply  tends  to  carlessness  in  its 
application  and  consequent  waste.  Where  liberal  and  old 
water  rights  are  provided,  it  is  frequently  the  practice  to 
turn  the  water  upon  the  land  and  permit  it  to  run  without 
change  or  attention  throughout  the  night  ana  sometimes 
during  the  day,  a  large  volume  of  water  soaking  into  the 
soil  without  benefit  to  the  crop." 

"The  duplication  of  ditches  is  another  fruitful  source  of 
waste,  reducing  the  duty  of  the  volume  of  water." 

"Reference  to  some  of  the  maps  prepared  by  this  depart- 
ment, will  show,  in  different  localities  several  ditches  par- 
alleling each  other  at  inconsiderable  distances  apart,  the 
upper  one  of  which  could  be  made  to  answer  the  purposes 
of  all  with  marked  economy  in  water,  as  well  as  large  sav- 
ing in  capital." 

"Too  little  attention  has  been  given  to  the  proper  prepara- 
tion of  the  surface  to  facilitate  the  rapid  spreading  of  the 
water." 

"This  is  principally  the  result  of  too  large  individual  own- 
ership ©f  land,  rendering  it  impracticable  to  give  close  sup- 
ervision and  secure  careful  preparation  of  the  land.'' 

"The  best  results  will  be  obtained  from  small  proprietary 
rights  in  land,  and  a  consequent  higher  state  of  cultivation." 

The  ownerships  of  the  cultivated  lands  of  the  state 
should  be  multiplied  by  ten  and  the  population  increased  to 
that  extent." 

All  that  is  here  stated  will  apply  with  equal  force  to  Da- 
kota, and  he  who  would  meet  with  the  greatest  measure  of 
success  will  heed  the  cautions  thus  held  out  by  so  high  an 
authority. 

Become  an  expert  in  irrigation  by  studying  up  from  all 
available  sources.  Profit  by  the  past  experiences  of  others. 
Beware  of  attempting  more  than  your  means  or  experience 
will  fully  warrant  and  conserve  well  the  supply  of  liquid 
wealth  so  freely  granted  you. 

The  following  table  will  serve  to  show  the  great  range  of 
duty  in  the  same  state,  and  as  a  very  valuable  basis  of  com- 


46 

parison  with  our  own  more  favorable  and  less  fluctuating 
climatic  conditions. 

TABLE  NO.  15. 

TABULATED     STATEMENT     OF     WATER-DUTY    ON    STREAMS 
INDICATED  FOR  1889  AND  1890. 


g  A  •£    i    .a 

£ 

03 

o 

o, 

£  .£  "-' 

It 

09 

ui 

1 

5C 

fe 

CK 

-      r 

03 

O 

STREAMS  GAUGED. 

jf.sl 

2 

si 

p 

| 

03^ 

.sl 

^™*>  1 

°g     1?  '    II 

*8 

lallj   gl  |  fi  ;   il 

3 

-l^S 

c  o 

^ 

w 

H 

fi 

Cache  La  Poudre  j    1890 

735.97 
770.51 

139,222 
139,222 

1.178 
1.254 

0.682 
0.338 

1.860 
1.592 

189.168 

180.687 

Big  Thompson        ..     j    jjgjj' 

214.53 
425.42 

91,037 

89,790 

0.579 
1.192 

no  data 
no  data 

424.35 
211.06 

St.  Vrain  j    Jig- 

215.46 

284  238 

94,013 
q  i  qcjr; 

0.563 
0  739 

0.532 

i'.oiV, 

436.33 
33'^  69 

South.     Boulder     andj    1889! 

461  !  97 

y-fc.o  j.» 
77^682 

l!406 

168!  15 

Boulder  Creek.  .  .  .  I   1890. 

419.33 

76,682 

1.34     1182.86 

Bear  Creek  j   J|®' 

60.40 
33.98 

10,173 
8,112 

1.4tJ     16v42 
1.03    1  ;  ^39.0-3 

From  1890  Report  of  State  Engineer  of  Colorado. 

It  will  be  noted  that,  in  all  the  above'  cited  estimates,  the 
water  is  that  of  a  natural  stream  the  volume  of  which  is 
largely  augmented  by  seepage  water.  The  water  haying 
been  used  at  a  higher  level,  seeps  through  the  soil  and  finds 
its  way  back  into  the  stream  at  a  lower  level,  there  to  be 
used  again  and  again,  thus  raising  the  duty,  over  a  given 
area,  of  a  given  original  volume. 

In  the  level  lands  of  the  Dakotas,  and  on  the  purely  in- 
dividual system  of  irrigation  which  will  prevail  here,  no 
account  need  be  taken  of  seepage  waters  as  a  source  of 
secondary  supply;  although  the  presence  of  seepage  water, 
and  the  power  of  the  soil  to  retain  it,  will  go  far  towards 
determining  the  ultimate  duty  of  the  original  well-supply. 

Quoting,  again,  from  the  Colorado  report  of  1888,  Engineer 
Greene  says,  "it  is  thought  that  when  distributed  with  the 
greatest  care,  and  in  sufficient  quantities  to  be  handled 
without  great  waste,  during  seasons  of  average  rainfall  and 
to  crops  and  soils  fairly  conditioned  to  its  economical  use, 
that  the  duty  of  water  should  approach  90  acres  to  the  sec- 
ond foot." 

Also  "Two  cubic  feet  of  water  per  second  carried  on  to  a 
field  in  one  body,  will,  under  conditions  otherwise  the  same, 
irrigate  more  than  twice  the  area  that  one  cubic  foot  carried 
alone  would  irrigate. 

What  will  be  the  conditions  of  the  duty  of  water  under 
the  Dakota  well-system,  and  what  the  duty  that  may  be 


47 

safely  relied  upon  under  average  conditions  y  Note  that 
the  average  rain-fall  for  10  years  has  been  21.58  inches;  the 
maximum  28.12  inches,  and  the  minimum  14.68  inches. 

In  this  level  country  a  rain-fall  of  24  inches  is  sufficient  to 
give  abundant  returns,  and  even  less  than  that,  with  proper 
distribution  and  provided  the  soil  could  be  maintained,  year 
after  year,  up  to  a  proper  standard  of  saturation.  For  the 
sake  of  conservatism,  reduce  the  average  annual  rain-fall  to 
18  inches,  instead  of  21  inches,  then  but  6  inches  need  be 
artificially  supplied  to  give  the  maximum  of  24  inches 
required ." 

Thus  6  inches  may  be  taken  to  fairly  represent  the  unit  of 
duty  required  in  Dakota. 

One  cubic  foot  per  second =448. 83  gallons  per  minute. 
This  amount  is  equaled,  or  exceeded,  by  most  of  the  small- 
er wells  of  the  state . 

One  second-foot =10,368,000  cubic  feet  in  4  months,  (which 
may  be  said  to  cover  the  irrigation  season,  from  April  to 
J  ulyj  or  a  sufficient  volume  to  cover  238  acres  a  foot  deep, 
or  476  acres  6  inches  deep.  476  acres  may,  therefore,  be  said 
to  be  the  duty  of  a  second-foot  in  that  period  of  time. 

Allowing  for  deep  seepage  and  evaporation,  and  call  the 
actual  duty  320  acres,  instead  of  476  acres  (a  loss  of  156 
acres),  and  it  would  appear  that  a  second  foot  is  amply 
sufficient  to  serve  a  half  section  of  land  during  a  poor  year. 

Account  is  not  here  taken  of  the  fact  that  during  the 
months  prior  to  the  beginning  of  the  irrigation  season,  the 
land  may  be  prepared,  by  flooding,  to  such  an  extent  as  to 
render  further  service  during  the  irrigation  season  almost 
unnecessary;  and  the  further  fact,  that,  by  a  system  of  res- 
ervoirs, an  enormous  volume  may  be  stored  to  supplement 
the  supply  of  the  well  itself  during  the  4  months  of  irriga- 
tion service.  Thus  the  supply  of  the  well  during  eight 
months  of  the  year  may  be  utilized  to  swell  the  duty  of 
the  well  during  the  4  months  of  service,  to  the  extent  of 
making  the  duty  during  that  period  extend  over  fully 
double  the  area  above  assumed  to  represent  the  estimated 
duty. 

The  difference  in  the  uniformity  of  supply  of  the  Colora- 
do rivers  and  the  Dakota  wells  is  most  marked.  The  1890 
gauging  record  of  the  Cache  La  Poudre  river  shows  that  the 
volume  discharged  during  March  varied  from  50  to  150 
cubic  feet  per  second.  During  April,  from  75  to  500  cubic 
feet;  increasing  thence  rapidly  to  June  2d,  when  the  dis- 
charge was  1825  cubic  feet.  The  decrease  was  then  quite 
rapid  until  the  first  of  September,  when  it  had  fallen  to  less 
tf>an  100  cubic  feet,  and  it  so  remained  during  the  balance 
of  the  season  of  discharge.  The  same  is  true  of  all  other 
western  rivers  whose  waters  are  derived  from  the  melting 
snows  of  the  mountains. 


48 

There  is  therefore  little  chance  to  use  the  waters  for  pur- 
pose of  irrigation  except  during  the  season  of  flood,  or,  in 
exceptional  cases,  where  the  waters  are  impounded  in  stor- 
age basins  of  great  area.  In  Dakota,  on  the  contrary,  the 
supply  is  constant  the  year  around.  Winter  and  summer 
the  flood  pours  forth  with  unabated  energy,  and  the  irrigat- 
or  may — as  he  actually  does — work  in  mid  winter,  with  a 
hoe  in  his  hand  and  a  fur  coat  an  his  back. 

By  reason  of  this  periodicity  the  duty  of  the  Colorado 
waters  is  limited  to  the  actual  duty  during  the  irrigation 
season,  and,  contrariwise,  the  duty  of  the  Dakota  well 
should  be  measured  by  what  might  be  fairly  called  its  annu- 
al duty. 

I  have  little  doubt  but  that  the  duty  of  the  s<  cond-foot 
in  Dakota  will  be  found,  in  the  end,  to  be  nearer  640  acres 
than  320  acres;  but  if,  for  the  present,  the  lesser  unite  be 
adopted  abundant  alowance  may  be  claimed  and  the  claim 
be  entitled  to  fair  consideration  by  reason  of  .its  actual 
conservatism . 

From  table  No.  20,  of  second  feet  reduced  to  gallons  per 
minute,  the  following  table  may  be  constructed  on  the 
basis  of  a  duty  of  but  320  acres  per  second-foot. 

TABLE  NO.  16. 

DUTY  OF  WATER  IX  DAKOTA. 


Gallons  per 
minute  from 
well. 

Equivalent 
in  second  ft. 

Duty  in 
acres. 

Gallons  per 
minute  from 
well. 

Equivalent 
in  second  ft. 

Duty  in 
acres. 

448 

1 

320 

2692 

6 

1920 

897 

2 

640 

3141 

7 

2240 

1346 

3 

960 

3590 

8 

2560 

1795 

4 

1280 

4039 

9 

2880 

2244 

5 

1600 

4488 

10 

3200 

i 

49 

THE  DIVISION  AND  MEASUREMENT  OF 
WATER. 

it  has  be^n  stated  by  Prof.  L.  G.  Carpenter,  in  his  work 
on  the  above  subject,  that  "one  of  the  most  important,  as 
well  as  one  of  the  most  difficult  problems  of  irrigation  is 
that  of  making  a  just  distribution  of  water."  Reference 
being  made  to  the  distribution  of  irrigation  waters  in  Col- 
orado and  elsewhere  where  irrigation  is  carried  on  on  a  vast 
scale  and  by  means  of  waters  taken  from  large  ditches  or 
canals  which  serve  a  large  area  and  are  supplied  from  rivers 
or  great  storage  reservoirs  in  the  mountains. 

Every  device  which  the  ingenuity  of  the  centuries  could 
devise  has  been  used  to  render  this  division  more  equitable, 
certain  and  economical  and  to  prevent  waste  where,  as  is 
usually  the  case,  the  economy  of  water  is  of  the  first  im- 
portance. 

The  literature  of  the  subject  is  voluminous,  but  the  Da- 
kota farmer  will  look  far,  and  in  vain,  for  any  information 
touching  upon  conditions  similar  to  his  own/ 

We  have  here  no  vast  system  of  canals,  nor  will  we  have 
in  the  future;  no  vast  storage  basins  and  no  need  of  the 
many  devices  used  in  other  sections  for  the  division  and 
measurements  of  water.  Our  system  is  essentially  individ- 
ual, but  the  day  is  at  hand  when  certain  simple  devices  will 
be  required  to  divide  the  waters  of  our  wells  among  the  few 
consumers  under  service  by  each  well  operating  under  the 
township  well  law,  or  among  those  who  rent  water  from  the 
individual  owners  of  a  well. 

With  us,  too,  it  is  not  wholly  a  matter  of  device  for  the 
mere  measurement  of  a  given  volume,  or  a  question  as  to 
the  unit  of  volume;  but  very  largely  a  matter  of  legislation 
based  upon  our  peculiar  conditions  and  needs,  which  legis- 
lation has  yet  to  be  evolved  and  put  to  the  test  of  practice. 

Contract,  too,  will  enter  largely  into  the  matter  of  the 
division  of  water  and,  on  the  start,  the  terms  will  be  more 
varied  and  uncertain  than  the  devices  necessary  to  carry 
them  out.  With  the  Dakota  farmer,  as  with  farmers  else- 
where, the  central  idea  will  be  to  secure  the  greatest  possi- 
ble service  from  the  water  at  hand ;  and  the  prevention  of 
waste  will  soon  demand  attention. 

In  the  irrigation  operations  of  the  west  all  the  elements 
are  predetermined.  The  water  supply  is  known,  the  ditches 
or  canals  are  constructed  of  a  certain  size  to  perform  a  cer- 
tain service  or  serve  a  given  area.  This  service  cannot  well 
be  exceeded  and  great  economy  must  be  observed  in  order 
that  the  actual  service  may  equal  the  calculated  service. 
Here— the  main  chanel  or  source  of  supply  is  the  well,  the 
volume  of  which  is  easily  determined.  The  fountain  head 
may  be  inexhaustible  but  only  so  much  can  be  drawn  off. 
The  farmer  may  have  a  surplus  which  he  may  waste  or 


50 

sell  to  his  neighbor,  in  which  case  economy  in  his  own  use 
and  in  theirs  will  operate  to  increase  his  revenue  from  the 
sale  of  the  surplus. 

So,  too,  in  the  operation  of  the  township  wells.  The  great- 
est service  will  be  desired  for  each  consumer  and  the  well 
will  be  called  upon  to  serve  as  many  consumers  as  possible. 
In  the  latter  case,  as  in  the  case  of  an  individual  owner, 
proper  service  to  each  consumer  can  only  be  had  through 
the  medium  of  a  storage  reservoir;  for  if  a  well  will  not— 
on  the  instant— serve  one  consumer  fully  it  will  certainly 
fail  to  serve  several  consumers. 

EACH  MUST  HAVE  HIS  OWN  RESERVOIR. 

Herein  will  arise  questions  as  to  the  manner  of  service, 
priority,  etc. 

Suppose  a  well  serves  four  quarter  sections  (say  the  E.  J^ 
of  Sec.  1  and  the  E.  ^  of  Sec.  12)  and  that  by  reason  of  the 
slope  of  the  ground  it  is  necessary  to  locate  the  well  on  the 
center  of  the  N.  E.  JC  of  section  1.  If  the  water  is  carried 
in  a  ditch  to  the  other  quarters,  and  the  amount  delivered 
is  measured  at  the  well,  the  owner  of  the  S.  E.  J£  °f  ^ec-  12 
would  receive  far  less  water  than  the  owner  of  the  ]S\  E.  J£ 
of  Sec.  1  because  of  the  far  greater  loss  by  evaporation  and 
seepage.  His  loss,  too,  would  be  his  neighbor's  gain. 

If  the  water  be  distributed  in  a  pipe  line  the  loss  of  head 
due  to  friction  in  the  longer  pipe  would  operate  to  the  same 
end  but  to  a  lesser  extent. 

Again— if  each  consumer  measures  his  water  at  the  point 
of  delivery  in  his  own  reservoir  a  question  will  arise  as  to 
the  priority  of  service.  A  may  fill  his  reservoir  first  and  D 
last,  but  meanwhile  the  water  in  A's  reservoir  has  been  low- 
ered a  foot  or  two  by  evaparation  and  seepage  and,  at  the 
period  when  greatest  service  is  required,  A  may  receive  20 
per  cent  less  service  than  D,  yet  each  has  received  and  paid 
for  the  same  volume  of  water.  If  the  service  to  the  several 
reservoirs  is  by  pipe  line  and  is  simultaneous  the  inequali- 
ties will  be  less  and  more  easily  subject  to  regulation. 

It  is  not  the  intention  here  to  raise  any  question  as  to  the 
details  of  distribution  or  the  possibility  of  an  equitable 
division  of  the  water;  nor  the  purpose  to  suggest  remedies 
for  anticipated  controversies,  but  it  must  be  known  that 
questions  of  detail,  such  as  those  above  suggested,  will  arise 
and  demand  a  solution.  When  they  do  a  solution  will  be 
found  on  lines  of  equity  to  all  interests. 

Notwithstanding  our  conditions  are  so  wholly  different 
from  those  met  elsewhere,  the  measurement  of  the  volume 
of  our  wells  must  be  treated  the  same,  however  much  the 
final  divisions  of  the  waters  may  differ. 

Heretofore  too  little  attention  has  been  paid  to  the  accu- 
rate determination  of  the  volumes  of  our  wells.  Usually 
the  volume  has  been  guessed  at  or  an  approximate  estimate 
has  been  made  by  timing  the  filling  of  a  barrel,  hogshead  or 


51 

tank.  In  some  cases  the  stream  has  been  weired  and  an  ac- 
curate estimate  made  as  to  the  volume. 

In  a  few  cases  grossly  exagerated  reports  have  been  cir- 
culated as  to  the  volume  of  certain  wells  (notably  the  Risdon 
WP!!  at  Huron,  which  has  been  advertised  as  having  a  vol- 
ume of  10.000  gallons  per  minute,  whereas  its  true  volume 
is  but  2,250  gallons  per  minute.) 

.  Such  exagerations  can  only  result  in  harm  and  should  be 
discouraged.  The  truth  is  sufficiently  wonderful  to  satisfy 
the  most  exacting. 

UNITS  OF  MEASUREMENT. 

THE  STATUTE  INCH,  is  a  unit  of  water  measurement 
much  used  in  the  western  states  and  territories.  It  varies 
in  different  states  and  even  in  different  sections  of  the  same 
state.  It  is  equal  to  about  45  cubic  inches  per  second.  One 
second  foot =38.4  statute  inches  in  Colorado.  This  unit  is 
practically  the  same  as  the  miner's  inch  it  being  the  miner's 
inch  in  the  terms  of  a  specific  statutory  specification.  It 
varies  in  different  states. 

THE  MIXER'S  INCH  Is  fully  explained  and  illustrated 
in  tables  18  and  19  and  the  accompanying  notes  and  figures. 
When  defined  by  state  law  it  is  known  as  the  statute  inch. 

THE  ACRE  FOOT  is  equal  to  43,560  cubic  feet  or  such  an 
amount  as  will  cover  one  acre  to  a  depth  of  one  foot  (See 
table  21  and  notes  &  P.  60).  This  unit  is  more  largely  one 
of  service  than  of  measurement. 

THE  SECOND  FOOT,  or  cubic  foot  per  second,  (See 
table  20  and  note  following.)  is  a  unit  definite  as  to  both 
volume  and  time  and  is  the  one  upon  which  all  wier  tables 
are  constructed  and  is  no  doubt  the  coming  unit  in  this 
and  other  countries. 

GALLONS  PER  MINUTE.  Like  the  second  foot  this 
unit  is  definite  as  to  both  volume  and  time  and  is  the  one 
commonly  used  in  Dakota.  (See  tables,  19  20,  36  and  37.) 

Two  general  methods  have  been  adopted  in  the  division 
and  measurement  of  water. 

THE  FIRST  is  known  as  the  DIVISOR,  the  object  of 
which  is  to  divide  the  waters  of  the  ditches  or  streams  into 
certain  proportionate  parts  among  consumers.  The  idea  is 
not  to  measure  according  to  some  fixed  unit  but  simply  to 
divide  or  proportion  the  water  according  to  a  certain  ratio. 
J^  to  each  of  two  consumers;  %  to  each  of  three,  &c  &c 

THE  SECOND  is  known  as  the  MODULE  the  purpose  of 
which  is  not  to  divide  but  to  measure  according  to  some 
fixed  unit.  In  Spain,  Italy  and  India  measuring  devices  or 
modules  have  been  in  use  for  centuries  but  of  late  years 
they  have  reached  their  greatest  perfection  in  our  western 
states 

Of  all  measuring  devices  the  WEIR  has  proved  to  be  the 
most  acurate  and  satisfactory.  (See  the  following  table  of 
weir  measurements,  table  17-) 

The  rectangular  weir  wherein  the  crest  is  horizontal  and 
the  sides  vertical  is  the  common  form  and  the  one  to  which 


52 

the  tables  herein  given  apply.  The  trapezoidal  weir  has  the 
crest  horizontal  and  the  sides  sloping;  this  form  possesses 
certain  advantages  which  will  not,  however,  be  considered 
here.  The  triangular  weir  or  notch  is  likewise  claimed  to 
possess  certain  advantages  over  other  forms. 
THE  SPILL  BOX. 

Among  the  most  satisfactory  devices  for  the  division  and 
measurement  of  water  is  the  excess  weir  or  spill-box,  myentf- 
ed  by  Mr.  A.  D .  Fopte  of  Idaho  and  illustrated  in  Fig.  6, 
wherein  A  is  the  main  ditch  the  now  in  which  may  be  check- 
ed by  gate  B  thus  forcing  a  portion  of  the  water  into  the 
spill-box  D  which  has  an  opening  F  in  the  side,  the  discharge 
through  which  into  the  lateral  ditch  Gr  is  regulated  by  a 
slide  and  graduated  scale  as  shown.  The  inner  edge  E  E  of 
the  box  is  lower  than  the  ends  and  outer  side  so  that  all 
water  not  passing  through  the  opening  F  spills  back  into 
the  main  ditch.  The  head  or  height  of  the  water  above  the 
opening  being  regulated  by  the  height  of  the  edge  E  E. 

By  this  means  the  head  at  the  opening  F  is  maintained 
constant  at  all  stages  of  the  water  in  the  main  ditch  and  the 
amoun  of  water  discharged  through  an  opening  of  any 
length  is  not  subject  to  fluctuations  due  to  change  of  head 
but  remains  constant.  Not  over  a  foot  of  fall  need  be  lost 
to  the  main  ditch  by  using  this  device.  The  spill  edge  E  E 
should  be  beveled  to  give  a  sharp  edge,  on  the  box  side,  over 
which  the  water  may  flow  without  friction.  This  form  of 
module  will  find  a  wide  field  of  usefulness  in  Dakota  as  the 
practice  of  irrigqtion  becomes  more  general  and  its  details 
more  closelv  considered. 


Fig.  6.    Spill  Box. 

THE  KECTANGULAK  WEIR 

This  form  of  module  or  measuring  device  haying  been  the 
subject  of  the  most  exhaustive  investigation,  is  considered 
to  be  the  best  suited  to  the  accurate  measurement  of  water. 

The  conditions  of  its  proper  operations  are : 
1st.    That  the  crest  shall  be  horizontal  and  the  sides  vertical. 
2d.      That  the  up-stream  face  be  vertical. 
3d.      That  both  the  crest  and  sides  be  sharp  edges  on  the  up-stream  side. 


4th.     That  the  depth  of  water  flowing  over  the  weir  be  not  less  than  3  not- 
more  than  25  inches 
5th.    That  the  depth  of  water  flowing  over  the  crest  be  not  greater  than 

1:i  the  length  of  the  weir. 

6th.    That  the  weir  opening  be  not  over  -'.-,  the  width  of  the  stream  ap- 
proaching it. 
7th.     That  the  discharge  over  the  weir  should  be  free  and  the  approach  of 

the  water  without  velocity  sufficient  to  produce  eddies. 
8th.    That  the  distance  from  the  crest  to  the  bottom  of  the  channel— and 
from  the  ends  of  the  weir  to  the  sides  of  the  channel,  shall  be  at  least 
twice  as  great  as  the  depth  of  the  water  flowing  over  the  weir.    This  is 
to  secure  complete  contraction. 

Weirs  may  have  either  partial  or  complete  contraction  as 
illustrated  by  figures  1  to  5  of  Fig.  7. 


Fig.  7.    Illustrating  Contraction  on  Weirs. 

In  following  over  a  weir  water  takes  the  form  shown  in  Fig 
1.  The  upward  movement  of  the  water  toward  the  crest  A 
of  the  weir  A  B  causing  the  water  to  arch  upward  as  shown. 
The  true  head,  as  shown  at  c,  is  reduced  by  the  downward 
curve  of  the  water,  as  shown  at  d  e.  This  is  called  the  con- 
traction. If  the  weir  has  the  form  shown  in  Fig.  2  the  con- 
traction of  the  flow  will  be  but  partial;  that  is,  there  will 
be  contraction  at  the  crest  a  c  but  none  at  the  sides  a  b 
and  c  d  past  which  the  water  flows  as  shown  in  Fig.  4. 
If  the  weir  has  the  form  shown  in  Fig.  3  the  contraction  is 
said  to  be  complete,  for,  in  addition  to  the  contraction  at 
the  crest,  there  is^also  contraction  at  each  side,  a  b  and. 
where  it  is  seen  that  the  width  of 
is  less  than  the  width  of  the 
illustrate  not  only  the  action  of 
meaning  of  the  term  "Complete 

Contraction."  which  is  a  requisite  to  the  proper  application 
of  the  following  table  of  weir  measurements. 
TO  CONSTRUCT  A  WEIR  AND  MEASURE  THE  VOL- 
UME OF  A  WELL. 

Select  some  convenient  point  where,  by  throwing  up  a 
low  bank,  a  small  pond  may  be  formed  by  the  stream  from 
the  well.  Across  the  outlet  set  aboard  or  plank  out  of 
which  has  been  cut  a  rectangular  piece  (say  12  inches  deep 
by  4  feet  long).  Support  the  board  by  nailing  to  stakes 
driven  into  the  ground  taking  care  that  the  edge  of  the 


c  d,  as  shown  in  Fig.  5 
the   outflowing  stream   a 
opening    b.     This  will 
flowing   water   but  the 


54 

opening  is  level  or  horizontal.  Make  the  bank  water-tight 
about  the  bottom  and  ends  of  the  weir.  Drive  a  stake  sev- 
eral feet  back  of  the  weir  and  near  the  edge  of  the  pond 
making  the  top  of  the  stake  level  with  the  crest  of  the  weir 
either  by  using  a  level  <  r  by  driving  the  stake  to  water 
level  at  the  moment  the  water  begins  to  spill  over  the  weir. 


55 

Permit  the  water  to  rise  to  the  full  height  at  which  it  will 
stand  while  flowing  over  the  weir.  Then  fueasure  the  depth 
of  water  over  the  stake. 

Enter  the  weir  table  writh  this  depth  (as  explained  in  ex- 
amples given)  and  get  the  quantity  for  one  inch.  Multiply 
this  quantity  by  the  length  of  the  weir  in  inches  to  get  the 
total  volume  flowing  from  the  well,  in  cubic  feet  per  minute. 

If  possible  have  the  up-stream  edges  of  the  weir  lined 
with  strips  of  tin  or  sheet  iron  to  give  a  sharp  edge  for  the 
water  to  flow  over,  if  this  is  not  at  hand  then  bevel  the 
crest  and  sides  of  the  weir  to  a  sharp  edge  on  the  up-stream 
side.  See,  in  short,  that  ALL  the  conditions  mentioned  on 
page  52  have  been  complied  with.  The  manner  of  con- 
structing and  using  a  weir  is  illustrated  on  the  opposite 
page,  where  A  is  the  weir  board  with  the  beveled  notch  or 
opening  B.  E  is  the  stake  driven  back  to  the  side  of  the 
weir,  out  of  the  current,  and  from  which  the  true  depth  is 
taken  as  shown. 

Application  of  Weir   Table  ]Vo.  17. 

This  table  gives  the  number  of  cubic  feet  of  water  passing 
per  minute  over  each  inch  in  width  ot  a  weir,  and  lor  depths 
from  -jJg-  inch  to  25  inches. 

The  top  horizontal  line  of  fractions  are  the  fractions  of  an 
inch  in  depth,  and  the  columns  of  figures  at  the  rig-.t 
and  left  ends  indicate  the  full  inches  of  depth.  The  quan- 
tities inside  the  table  are  the  cubic  feet  discharged. 

Thus  /5  inch  of  depth  =  .11  cu.  ft.  per  inch  width  of  weir,  f  See  at  "1 
10  inches  "  "  =12.71  "  "  .  "  "  "  «•'*****  • 
lOii  \"  '••  "  =13.19  "  "  "  "  "  "  }  in  the  J 
16H  "  "  "  =27.43  "  "  "  '«  "  "  L  table  J 

These  examples  will  render  clear  the  use  of  the  table 

Examples  of  Use.  How  many  cubic  feet  and  gallons  are 
discharged  per  minute  by  a  well  the  water  of  which,  in  flow- 
ing over  a  weir  5  feet  long,  shows  a  depth  of  7%  inches? 

From  table  the  quantity  of  water  for  one  inch  wide  by  7% 
inches  deep=8.05  cubic  feet  per  minute;  5  feet  wide=60 
inches;  therefore  8.05  multiplied  by  60^483  cubic  feet  per 
minute.  Referring  to  table  No.  36  we  find  that  483  cubic 
feet=3612.8  gallons.  Therefore  by  this  simple  process  the 
volume  of  our  well  per  minute  has  been  found  to  be  483  cu- 
bic feet,  or  3612.8  gallons  per  minute. 

The  work  involved  in  the  construction  of  a  weir  is  but 
slight,  and  the  calculation  of  the  flow,  as  above,  is  a  mere 
matter  of  multiplication  and  addition.  Every  well  owner 
should  see  that  the  volume  of  his  well  is  accurately  deter- 
mined in  this  way;  and  not  once  alone,  but  every  few 
months,  in  order  to  know  whether  there  is  any  increase  or 
diminution  in  the  flow.  A  series  of  suck  systematic  tests 
would  no  doubt  result  in  furnishing  valuable  information 
leading  up  to  a  correct  determination  as  to  the  source  and 
supply  of  the  artesian  stream. 


TABLE  NO.  17. 

AVIER  MEASUREMENTS. 


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57 

Certain  re tinements  of  calculation  enter  into  the  matter 
of  measurement  by  weirs,  but  they  have  not  sufficient  bear- 
ing on  the  ordinary  practice  to  deserve  more  than  mention 
here.  Tables  of  weir  measurements  are  constructed  where- 
in these  elements  have  been  taken  into  account,  but  the 
table  given  is  sufficiently  accurate  for  our  use.  In  view  of 
the  fact  that  the  table  given  may  not  meet  all  the  require- 
ments of  practice  the  formula  upon  which  the  most  accurate 
weir  measurements  are  based  is  here  given  and  briefly 
explained.  The  weir  formula  of  Francis  is  as  follows: 

y=C  (L-.2  H)  Hf 

Wherein  V= Volume  in  cu  ft  per  sec.  flowing  over  the  weir 
C=The  coefficient  of  discharge  (=3.33)  (or  3.3333+) 
L=The  length  of  the  weir  in  feet. 
H=The  head,  or  depth  of  water  over  the  weir, 
f =The  square  root  of  the  cube  of  H. 

Substituting  the  value  of  C,  the  formula  becomes, 
V=3.33  (L— ,2H)  Hf 

Which  reads  as  follows: 

Volume  per  second— 3.33  multiplied  by  (the  length  of  the 
weir  less  two  tenths  of  the  head)  multiplied  by  the  square 
root  of  the  cube  of  the  head. 

This  will  be  rendered  plain  by  an  illustration. 

What  will  be  the  discharge  per  second  over  a  weir  JO  feet 
long  if  the  water  is  1.5  feet  deep? 

The  total  length  L  of  the  weir  is  reduced,  by  reason  of  the 
contractions  at  the  ends,  to  the  calculated  amount  of  ^  of 
the  depth,  or  head,  for  each  contraction,  hence  the  expres- 
sion (L— .2H) 

In  the  example  the  depth=1.5  feet,  ^  of  which  (there 
being  2  contractions)  is=.3,  and  ten  feet— the  full  length— 
less  .3=9.7  feet,  or  the  effective  length. 

The  cube  of  1.5  (the  head)  =3.375  and  the  square  root  of 
3.375=1.837 .     We  now  have  the  formula  thus: 
V=3.33X9.7X  1.837. 

Which  multiplied  through =59.39  cubic  feet  per  second 
flowing  over  the  weir. 

The  cubes  and  roots  in  these  calculations  may  be  taken 
directly  from  the  tables  given  elsewhere  herein.  This 
amount  is  somewhat  less  than  that  resulting  from  the  use  of 
the  weir  table,  but  the  table  is  sufficiently  accurate  for  all 
practical  uses.  The  use  of  the  formula  may,  in  some  cases, 
be  more  convenient  and  hence  it  has  been  given .  Ordinar- 
ily the  formula  is  given  thus. 

V=3.33  L  H« 

no  account  being  taken  of  the  loss  to  L  resulting  from  the 
end  contractions.  If  a  weir  is  used  wherein  there  are  no  end 
contractions  then  this  last  form  of  formula  would  be  used. 
If  the  opening  is  obstructed  by  a  central  post  there  would 
be  4  contractions  and  the  expression  of  the  formula  would 
be  (L— .4H),  and  so  on  for  any  othei  number  of  contractions, 


TABLE  NO.  18. 

TABLE  OF  MINER'S  INCHES 


Jleduced  to  Cubic  Feet  and  Gallons  and  to  Cub.  Ft.  and  Gals,  per  Minute. 
(Corresponding  with  the  "  Colorado  "  inch.)               New. 

Miner's 
Inches. 

Equivalent   in  Equiv.    in    cu. 
Cubic  Feet.    I  ft.  per  minute. 

Equivalent    in 
Gallons. 

Equiv.  in  Gals, 
per  minute. 

1 

.0259337 

1  .  556024 

.194 

11.64 

2 

.0518674 

3.112048 

.388 

23.28 

3 

.0778011 

4.668072 

.582 

34.92 

4 

.1037348 

6.224096 

.776 

46.56 

5 

.1296685 

7.780120 

.970 

58.20 

6 

.1556022 

9.336144 

1.164 

69.84 

7 

.1815359 

10.892168 

1.358 

81.48 

8 

.2074696 

12.448192 

1.552 

93.12 

9 

.2334033 

14.004216 

1.746 

104.76 

10 

.2593370 

15.560240 

1.940 

116.40 

20 

*           .52 

*       31.12 

*    3.88 

*    232.8 

30 

.78 

46.68 

5.82 

349.2 

40 

1.04 

62.24 

7.76 

465.6 

50 

1.30 

77.80 

9.70 

582.0 

60 

1.56 

93.36 

11.64 

698.4 

70 

1.82 

108.92 

13.58 

814.8 

80 

2.07 

124.48 

15.52 

931.2 

90 

2.33 

140.04 

17.46 

1047.6 

100 

25.93 

155.60 

19.40 

1164.0 

200 

51.87 

311.20 

*    38.8 

2328. 

300 

77.80 

466.80 

58.2 

3492. 

400 

103.73 

622.40 

77.6 

4656. 

500 

129.67 

778.01 

97.0 

5820. 

600 

155.60 

933.61 

116.4 

6984. 

700 

181.54 

1089.21 

135.8 

'     8148. 

800 

207.47 

1244.81 

155.2 

9312. 

900 

233.40 

1400.42 

174.6 

10476. 

1000 

259.34 

1556.02 

194.0 

11640. 

10000 

2593.37 

15560.24 

1940.0 

116400. 

*  Note  the  change  in  location  of  the  decimal  point  at  *  * 

Fig.  9.  The  Miner's  Inch  is  such  a  quan- 

Miner's   Inch    Measurement.  tity  of  water  ag  will   now  through 

1  an  aperture  one  inch  square  in  a 
board  two  inches  thick,  under  a 
head  of  water  of  6  inches,  in  one 
second  of  time  and  it  is  equal  to 
0.194  gallon,  or  11.64  gallons  per 
minute;  and  to  .0259337  cubic  foot, 
or  1.556024  cubic  feet  per  minute. 
Fig.  9  shows  a  trough  with  6  inches 
<HOLSI  9*.  depth  of  water  in  it,  and  with  a 
bottom  2  inches  thick  through  which  is  cut  a  hole  1  inch 
square.  If  the  depth  of  water  is  maintained  at  6  inches  one 
miner's  inch  per  second  would  be  discharged  through  the 
hole. 

This  unit  of  water  measurement  has  been  and  is  very  extensively  used 

guaging  of  streams 
.    By  reason 

miner's  kichT varies  in^differenTstates  from  1.36  to  1.173  cubic  feet  per  min- 
ute. The  head  varies  from  3  to  10  inches  and  in  some  cases  it  is  measured 
from  the  top  of  the  opening,  (in  the  side  of  the  box  or  flume)  in  other 
cases  from  the  bottom  and  in  still  other  cases— and  properly— from  the  cen- 
ter of  the  opening. 


59 

Then,  too,  the  volume  discharged  under  a  given  head,  and 
from  a  given  area  of  opening,  varies  as  the  form  of  the 
opening  is  changed—  thus,  36  miner's  inches  will  be  discharg- 
ed through  an  opening  one  inch  high  by  36  inches  long,  and 
also  from  an  opening  6  inches  high  by  6  inches  wide,  (the 
area  of  the  opening  being  the  same)  yet,  as  a  fact,  more 

water  will  flow  through  the  latter  opening  because  it  flows  with  less  re- 
sistance from  the  edges  of  the  opening.  In  the  first  case  the  edges  of  the 
opening  measure  74  inches,  while  in  the  second  case  they  measure  but  24  in. 
The  volume  discharged  is  further  varied  by  the  form  of  the  edge,  i.  e., 
whether  it  be  square,  rounded,  sharp  or  beveled  ;  and  further  still  by  the 
thickness  of  the  edge—  whether  it  be  one  inch  or  more.  It  bein^  manifest- 
ly impossible,  over  any  extended  area,  to  secure  any  uniformity  m  the  head 
of  water  maintained,  or  in  the  form  or  thickness  of  the  edges  of  the  outlet, 

or  in  the  ratio  of  the  area 
°f  opening  to  wet  perime- 
ter,  it  is  impossible  to 
maintain  any  standard  of 
value  for  the  miner's  inch 
except  within  the  limits 
stated.  The  Colorado  inch 
most  nearly  corresponds 
with  the  theoretical  dis- 
charge. The  California 
inch,  as  usually  measured. 
is  from  an  aperature  2 
and  inches  high  of  any 
desired  length,  though  a 
plank  1*4  inches  thick  as 


Fig.  10.  Miner's  Inch  Measurements. 
2  inches  above  the  bottom  of  the  flume.  This  secures  a  complete  contrac- 
tion of  the  stream.  The  value  of  the  inch  will  increase  as  the  orifice  is 
enlarged,  as  shown  hi  the  following  table. 

TABLE  XO.  19. 

TABLE  OF  MINER'S  INCH  MEASUREMENTS  . 

From  Pelton  Water  Wheel  Co. 


Length 

Opening  2  inches  high. 

Opening  4  inches  high. 

of 

Head  to 

Head  to 

Head  to 

Head  to    }    Head  to 

Head  to 

openi'g 

center  5 

center  6 

center  7 

center  5 

center  6 

center  7 

in 

inches. 

inches. 

inches. 

inches. 

inches. 

inches. 

inches. 

Cubic  ft.  [Cubic  ft. 

Cubic  ft. 

Cubic  ft. 

Cubic  ft. 

Cubic  ft. 

4~~ 

1.348 

1.473 

1.589 

.320 

.450 

1.570 

6 

1.355 

1.480 

1.596 

.336 

.470 

1.595 

8 

.359 

.484 

.600 

.344 

.481 

.608 

10 

.361 

.485 

.602 

.349 

.487 

.615 

12 

.363 

.487 

.604 

.352 

.491 

.620 

14 

.364 

.488 

.604 

.354 

.494 

.623 

16 

.365 

.489 

.605 

.a56 

.496 

.626 

18 

.365 

.489 

.606 

.357 

.498 

.628 

20 

.365 

.490 

.606 

.359 

.499 

.630 

22 

.366 

.490 

.607 

.359 

.500 

.631 

24 

.366 

.490 

.607 

.360 

.501 

.632 

26 

.366 

.490 

.607 

.361 

.502 

.633 

28 

.367 

.491 

.607 

.361 

.503 

.634 

30 

.367 

.491 

1.608 

.362 

.503 

.635 

40 

:367  \ 

.492 

1.608 

1.363 

.505 

.637 

50 

.368 

.493 

1.609 

1.364 

.507 

.639 

60 

.368  i 

.493 

1.609 

1.365 

.508 

.640 

This  table  shows  the  discharge  in  cubic  feet  of  each  miners'  inch  of  the 
openings  given  in  the  table.  For  an  opening  2  inches  high  by  20  inches 
long  and  5  inch  lead  the  total  discharge  per  minute  would  be  1.365X40=54.6 
cubic  feet.  (2  inches  by  20  inches =40  inches = area  of  opening.) 


60 

The  following  brief  table,  by  C.  L  Stevenson,  C.  E.,  of 
Salt  Lake  City,  shows  at  a  glance  the  relationship  between 
the  different  units  of  water  measurement  with  sufficient 
accuracy  for  ordinary  calculation.  It  will  be  valuable  for 
ready  reference. 

1  cu.  ft.  per  second  equals: 


2  acre  feet  in  24  hours. 
60  acre  feet  in  30  days. 
180  acre  feet  in  3  months. 
730  acre  feet  in  1  year. 


7 .5  gallons  per  second. 
449  gallons  per  minute. 
50  California  inches, 
38.4  Colorado  inches. 


100  California  inches  equal : 


4  acre  feet  in  24  hours. 
1  acre  foot  in  6  hours. 
120  acre  feet  in  30  days. 
360  acre  feet  in  3  months. 
1460  acre  feet  in  1  year. 

100  Colorado  inches  equal:  t 


15  gallons  per  second. 
900  gallons  per  minute. 
77  Colorado  inches. 
2  cubic  feet  per  second. 


5£  acre  feet  in  1  hour. 
1  acre  foot  in  4.2  hours. 
155  acre  feet  in  1  month. 
465  acre  feet  in  3  months. 
1,886  acre  feet  in  1  year. 

The  unit  of  the  miner's  inch  will  find  no  place  in  Dakota.  Mention  has 
been  made  of  it  here  because  it  is  so  extensively  used  elsewhere  and  is  so 
frequently  referred  to  in  the  irrigation  literature  of  the  day. 


19.5  gallons  per  second. 
1,170  gallons  per  minute. 
2.6  cubic  feet  per  second. 
130  California  inches. 


TABLE  NO.  20. 
"SECOND    FEET" 

REDUCED  TO  GALLONS. 

New. 


No.  of 
second 
feet. 

Equivalent 
in    gallons 
per  second. 

Equivalent 
in    gallons 
per  min'te. 

& 

1.87 

112.2 

ft 

3.74 

224.4 

& 

5.61 

336.6 

1 

7.48 

448  8 

2 

14.^6 

897  6 

3 

22.44 

1346!  4 

4 

29.92 

1795.2 

5 

37.40 

2244.0 

6 

44.88 

2692.8 

7 

52.36 

3141.6 

8 

59.84 

3590.4 

9 

67.32 

4039.2 

10 

74.80 

4488. 

20 

149.61 

8976. 

30 

224.41 

13464. 

40 

299.22 

17952. 

50 

374.02 

22440. 

60 

448.83 

26928. 

70 

523.63 

31416. 

80 

598.44 

35904. 

90 

673.24 

40392. 

100 

748.05 

44883. 

200 

1496.1 

89766. 

300 

2244.2 

134649. 

400 

2992.2 

179532. 

500 

3740.2 

224412. 

1000 

4780.5 

448330. 

NOTE. 

The  unit  of  water  measurement 
known  as  the  SECOND  FOOT  is  very 
largely  used  in  the  west  where  it  is  be- 
coming more  popular  because  it  is  a 
unit  whose  value  cannot  be  disputed. 
A  second  foot  is  one  cubic  foot  per 
second.  This  is  definite  as  to  a  deter- 
minable  volume  discharged  within  a 
determinable  time,  and  thus  is  estab- 
lished a  unit  most  capable  of  expres- 
sion in  the  terms  of  ordinary  calcula- 
tions. 

It  might  be  well  if  such  a  unit  were 
used  to  express  the  volume  of  our 
wells  but  the  unit  of  gallons-per-min- 
ute  has,  by  usage,  become  established 
and  it  will  probably  be  retained. 
Some  equity,  too,  may  be  urged  in  the 
retention  of  the  gallon  unit,  as  applied 
to  wells,  instead  of  the  adoption  of 
the  larger  unit  of  the  second  foot  which 
is  more  applicable  to  the  greater  -vol- 
umes to  which  it  is  applied  in  the 
greater  irrigation  operations  of  the  far 
west. 


61 
TABLE  NO.  21. 

VOLUME  AND  WEIGHT  OF  WATEK  ON  ONE  ACRE. 


New. 


Depth  in  Cubic  foot  of 
inches,    i       water. 

Gallons. 

Weight,  at  62.425  pounds  to  the 
cubic  foot. 

Tons           and           Pounds. 

1 

3630 

27153 

113 

603 

2 

7260 

54308 

226 

1206 

a 

10*90 

81462 

339 

1809 

\ 

14520 

1G8616 

453 

411 

5 

18150 

135771 

566 

1014 

6 

21780 

162924 

679 

1618 

7 

25410 

190079 

793 

220 

8 

29010 

217234 

906 

822 

9 

32670 

244388 

1019 

1424 

10 

36300 

271542 

1133 

27 

11 

39930 

298695 

1246 

630 

12 

43560 

325850 

1359 

1233 

Note:  For  amounts  less  than  1  inch  cut  off  one  place  to 
the  right  for  tenths  and  two  places  for  hundredths,  thus — 
For  1  inch  Cu.  ft.  =  363.0  and  Gals.  =  2715.3. 
"     .01     «        "        -  36.3    u        "        =  271.53 


Example:  Required  the  volume  for  fall  of  7.38  inches? 

7.  inches  =  25410  cu.  ft.  190,079    gallons. 
.3    "        =    1089        "  8,146.2 

.08  "        =      290.4     "  2,172.34      " 


7.38  "        =  26,789.4 


200,397.54 


1  ACRE  FOOT  =  43,560  cubic  feet,  or  sufficient  water  to 
cover  the  acre  to  a  depth  of  one  foot. 

This  unit  is  the  most  recent  of  the  units  of  water  measure- 
ment. The  element  of  time  is  entirely  eliminated  and  the 
element  of  volume  is  specifically  fixed  in  the  terms  of  the 
definite  unit,  the  cubic  foot. 

The  unit  is  largely  used  in  representing  the  capacity  of 
storage  reservoirs,  since  it  conveys  a  definite  or  comprehen- 
sible idea  as  to  the  service  of  the  water  stored.  To  say  that 
a  reservoir  will  hold  4,356,000  cubic  feet  conveys  but  little 
knowledge  to  the  average  man;  but  to  say  that  the  reservoir 
will  hold  100  acre  feet  of  water  conveys  at  once  the  idea  as 
to  the  service  which  will  be  rendered  by  the  impounded  wa- 
ter. The  unit  is,  therefore,  what  may  be  properly  termed  a 
SERVICE  UNIT,  and  it  fully  answers  this  purpose. 

The  last  column  of  Section  A,  of  Table  No.  34,  will  give 
the  cubic  feet  in  the  number  of  acre-feet  represented  by  the 
acres  of  the  first  column,  and  Section  B  the  corresponding 
number  of  gallons,  while  Section  C  will  show  the  time  re- 
quired for  wells  of  different  volumes  to  throw  this  amount 
of  water. 


62 

TABLE  NO.  22. 
From  Trautwiiie's  "  Civil  Engineer's  Pocket  Book." 


HYDRAULICS. 

TABLE  2.    Weight  of  Water  (at  62J4  Ibs.  per  cubic  foot) 
contained  in  one  foot  length  of  pipes  of  different  bores. 

(Original.) 


Bore. 
Ins. 

Water. 
Lbs. 

Bore. 
Ins. 

Water. 
Lbs. 

Bore. 
Ins. 

Water. 
Lbs. 

Bore. 
Ins. 

Water. 
Lbs. 

Ys 

0.005305 

4 

5.43234 

14% 

71.3843 

40 

543.234 

i 

0.021220 

4*4 

6.13260 

15 

76.3922 

42 

598.915 

0.047745 

41 

6.87530 

15% 

81.5699 

44 

657.313 

% 

0.084880 

4%! 

7.66044 

16 

86.9174 

46 

718.427 

/8 

0.132625 

5 

8.48803 

16% 

92.4346 

48 

782.257 

'AA 

0.190981 

5}4 

9.35805 

17 

98.1216 

50 

848.803 

/« 

0.259946 

6j5 

10.27051 

17% 

103.9783 

52 

918.065 

1 

0.339521 

5% 

11.22542 

18 

110.0048 

54 

990.044 

l% 

0.429706 

6 

12.22276 

18% 

116.2011 

56 

1064.738 

\\? 

0.530502 

6^ 

13.26254 

19 

122.5671 

58 

1142.149 

1% 

0.641907 

6i| 

14.34477 

19% 

129.1029 

60 

1222.276 

1% 

0.763922 

6% 

15.46943 

20 

135.8084 

62 

1305.119 

\% 

0.896548 

7 

16.63653 

21 

149.7288 

64 

1390.678 

ig 

1.039783 

7^ 

17.84608 

22 

164.3282 

66 

1478.954 

i>3 

1.193629 

7V2 

19.09806 

23 

179.6067 

68 

1569.946 

2 

1.358084 

7?4 

20.39249 

24 

195.5642 

70 

1663.653 

2^ 

1.533150 

8 

21.72935 

25 

212.2007 

72 

1760.077 

2H 

1.718826 

8^ 

23.10865 

26 

229.5163 

74 

1859.218 

2p 

1.915111 

8l| 

24.53040 

27 

247.5109 

76 

1961.074 

2.122007 

874 

25.99458 

28 

266.1845 

78 

2065.646 

2% 

2.339512 

9 

27.50121 

29 

285.5372 

80 

2172.935 

2% 

2.567628 

9% 

30.64178 

30 

305.5690 

82 

2282.940 

2/B 

2.806354 

10 

33.95211 

31 

326.2798 

84 

2395.661 

3 

3.055690 

10% 

37.43220 

32 

347.6696 

86 

2511.098 

3H 

3.315636 

11 

41.08205 

33 

369.7385 

88 

2629.251 

3*2 

3.586191 

11% 

44.90166 

34 

392.4864 

90 

2750.121 

3% 

3.867357 

12 

48.89104 

35 

415.9133 

92 

2873.707 

3% 

4.159133 

12% 

53.05017 

36 

440.0193 

94 

3000.008 

3% 

4.461519 

13 

57.37906 

37 

464.8044 

96 

3129.026 

3% 

4.774515 

13% 

61.87772 

38 

490.2685 

98  \  3260.761 

3J| 

5.098121 

14 

66.54613 

39 

516.4116 

100    3395.211 

The  weight  of  water  in  a  given  length  (as  one  foot)  of  any  pipe  or  other 
circular  cylinder  is  in  proportion  to  the  square  of  the  bore,  or 

inner  diameter.  Hence  the  weight  of  water  in  1  foot  length  of  any  cylinder  of 
other  diameter  than  those  in  the  table  can  be  found  by  multiplying  that  for  a  1 
inch  pipe,  0.339521,  by  the  square  of  the  inner  diameter  of  the  given  cylinder  in 
inches.  Thus,  for  a  cylinder  120  inches  diameter:  diameter2  =  1202  =  14400r 
and  weight  of  water  in  1  foot  depth  =  0.339521  X  14400  =  4889.10  Ibs.  Similarly, 
(A)2  =  A9S  =  0.191406,  and  0.339521  X 0.191406  =  0.064986  Ib.  =  weight  in  1  foot 
of  T7^  inch  pipe.  Here,  also,  r7^  =  half  of  J ;  hence,  weight  for  -^  inch  =  one- 
fourth  of  weight  for  |  inch  =  one-fourth  of  0.259946  =  0.064986. 

Weight  of  one  square  inch  of  water  1  foot  high,  at  62  J  IDS.  per 
cubic  foot  =  62.25  -j-  144  =  0.432292  Ib. 

For  further  information  respecting  weight  of  water,  see  page  E  61  &^6& 


63 


TABLE  NO.  23. 

TABLE  OF  WEIGHT  OF   WATER. 
Maximun  density  is  at  39.8°  Fahr. 


New. 


Cubic  feet.   = 

Pounds  . 

Gallons.      = 

Pounds. 

1 

62.425 

1 

8.  3216 

2 

124.850 

2 

16.6432 

3 

187.275 

3 

24.9648 

4 

249.700 

4 

33.2864 

5 

312.125 

5 

41.6080 

6 

• 

374.550 

6 

X 

49.9296 

7 

• 

4:36.975 

7 

•K- 

58.2512 

8 

* 

499.400 

8 

* 

66.5728 

9 

40 

561.825 

9 

•H 

74.8944 

10 

624.250 

10 

id 

83.2160 

20 

.2 

*    1248.50 

20 

a 

*    166.432 

30 

£ 

1872.75 

30 

249.648 

40 

Jj* 

2497.00 

40 

332.864 

50 

• 

3121.25 

50 

'« 

416.080 

60 

& 

3745.50 

60 

499.296 

70 

'G 

4369.75 

70 

'3 

582.512 

80 

"0 

4994.00 

80 

O 

665.728 

90 

«M 

5618.25 

90 

«w 

748.944 

100 

c 

6242.50 

100 

0 

832.160 

200 

ti 

c 

*    12485.0 

200 

g 

*    1664.32 

300 

18727.5 

300 

2496.48 

400 

"03 

24970.0 

400 

03- 

3328.64 

500 

J 

31212.5 

500 

| 

4160.80 

600 

£J 

37455.0 

600 

4992.96 

700 

43697.5 

700 

5825.12 

800 

s 

49940.0 

800 

g. 

6657.28 

900 

e 

56182.5 

900 

Of 
fl 

7489.44 

1000 

03 

r| 

62425.0 

1000 

<s 

9321.60 

2000 

0 

*    124850. 

2000 

1 

*    16643.2 

3000 

<£> 

rj 

187  275. 

3000 

0 

24964.8 

4000 

249700. 

4000 

£ 

33286.4 

5000 

1 

312  125. 

5000 

0> 

41608.0 

6000 

0 

374  550. 

6000 

d 

o 

49929.6 

7000 

^ 

436975. 

7000 

fe 

58251.2 

8000 

499400. 

8000 

66572.8 

9000 

561825. 

9000 

74894.4 

10000 

624250. 

10000 

83216.0 

100000 

6242500. 

100000 

832160.0 

1000000 

62425000. 

1000000 

8  321  600.0 

For  ordinary  purposes  the  weight  of  a  cubic  foot  of  water  may  be  taken 
to  be  62^  pounds.  The  weight  varies  with  the  temperature  as  shown  in 
the  following  table. 


Temperature 
Fahrenheit. 


Lbs.  per     | 
cubic  ft.     | 


Temperature 
Fahrenheit. 


Lbs.  per 
cubic  ft. 


32°  freezing. 

40° 

50° 


.62.417  |  70° 62.302 


.62.423 
.62.409 
.62.367 


80° 62.218 

90° 62.119 

212°   boiling 59.675 


Cubic  foot  of  ice  =  57.2  Ibs. 

Cubic  foot  salt  or  sea  water  =  64.31  Ibs. 

35.84  cubic  feet  of  water  weighs  one  ton. 

39.13    "  "        ice  "  "      " 

2.311  feet  of  water  =  1  lb.  per  square  inch. 

1  cubic  inch  of  water  =  .036024 lb.  approximately. 

1    "  "  «•        =  .576384  ounce. 

1  U.  S.  Pint  =  1.0402  lb.  of  water 

1  U.  S.  Quart  =  2.0804  lb.  of  water. 

1  U.  S.  Gallon  =  8.3216  lb.  of  water.  (8M) 

1  U.  S.  Wine  barrel— 31  ^  GaL  =  262.131  lb.  of  water. 

Trautwine  and  HaswelL 


TABLE  NO.  24. 
PRESSURE  OF  WATER. 


T&e  pressure  of  water  in  pounds  per  square  inch  for  every  foot  in  height  to 
500  feet;  and  then  by  intervals,  to  1000  feet  head.    By  this  table,  from  the  pounds 
pressure  per  square  inch,  the  feet  head  is  readily  obtained;  and  vice  versa. 

•MIL 

Prvwure 

-or 

P»et 

Prewure 

Feet 
Hewl. 

PreMura 

Feet 

peT^u'are 

r««t 

Preuure 

i 

0-43 

.65 

28.15 

129 

5588 

193 

83.60 

257 

11.32 

a  ' 

0.86 

66 

28.58 

56.31 

194 

8403 

258 

11.76 

3 

1.30 

67 

29  O2  . 

13* 

56.74 

84.47 

259 

12.19 

4 

i-73 

68 

2945 

132 

57.18 

196 

8490 

200 

12.62 

i 

2.J6 

2  59 

69 
70 

29.88 
30.32 

134 

57-61 
5804 

|$ 

85-33 
85  76 

26l 
2O2 

13.06 
13-49 

7 

3-03 

30.75 

5848 

199 

86.20 

263 

13.92 

•8 

3.46 

72 

136 

58.91 

200 

86.63 

264 

M.36 

9 

3-89 

73 

3^62 

137 

5934 

201 

87.07 

265 

14.79 

K? 

11 

4*76 

74 

75 

3205 
32.48 

138 
139 

59-77 
60.21 

202 
203 

87.50 
87.93 

266 
267 

15  22 
1566 

12 

520 

76 

3292 

140 

6064 

204 

88.36 

268 

16.09 

13 
14 

•13 

i 

3335 
3378 

14I 
142 

61.07 
61.51 

SS.So 
8923 

269 
270 

16.52 
16.96 

11 

^l 

6.49 
6-93 
7.36 

g 

si 

3465 
3508 

144 

61.94 
62.37 
6281 

207 
208 
209 

8966 
90  10 
90.53 

271 
272 
273 

'7-39 
17  82 
1826 

l8 

7-79 

82 

3552 

146 

63.24 

210 

90.96 

274 

18.69 

19 
20 

§22 

8.66 

i,3 

35-95 
36.39 

H7 
14S 

63.67 
64.10 

211 
212 

91  39 
91.83 

275 
276 

19  12 

21 

9.09 

85 

36.82 

149 

64.54 

213 

92.26 

2/7 

1999 

22 

953 

86 

37-25 

64.97 

2I4 

92.69 

27S 

20  42 

23 
24 

9.96 
10-39 

1 

3768 
3812 

152 

6540 
65.84 

215 
2l6 

93  13 
93.56 

279 

2SO 

20.85 
21.29 

25 

10.82 

89 

38.55 

153 

66.27 

217 

9399 

2Sl 

21.72 

36 

3 

11.26 
11.69 

90 
91 

3898 
3942 

154 

66.70 
67.14 

218 

219 

94-43 
94.86 

2S2 
-283. 

22.  IS 
22.59 

28 

12.12 

92 

39.85 

156 

67.57 

220 

95  30 

2S4 

23.02 

29 

13-55 

93 

40.28 

157 

68.00 

221 

95-73 

2SS 

2345 

3° 

12.99 

94 

40.72 

158 

68.43 

222 

96  16 

2S6 

TI 
3« 

13.42 
1386 

$ 

4i.i5 
41-58 

!lo 

6887 
69-31 

223 
224 

9660 
97-03 

287 

2SS 

24-75 

33 

14.29 

97 

42.01 

161 

69-74 

225 

97.46 

289 

25-18 

34 

14.72 

98 

4245 

162 

7017 

226 

97.90 

290 

25.62 

35 

15.  16 

99 

42.88 

163 

70.61 

227 

291 

26.05 

36 

i  v59 

100 

43  31 

164 

71-04 

228 

9876 

292 

26.48 

37 

It.  02 

1OI 

43-75 

ig 

71,47 

229 

9920 

293 

26  92 

38 
39 

16-45 
1689 

102 
103 

44.18 
44.61 

166 

167 

71,91 
72-34 

230 

99-63 
100.06 

294 
295 

27-35 

27.78 

40 

104 

45-05 

168 

72.77 

232 

loc  49 

296 

28.22 

4» 

17-75 

J05 

4548 

169 

73.20 

233 

10093 

297 

2S6c 

4* 

18.19 

106 

459i 

170 

73-64 

234 

101  36 

298 

29.08 

43 

18.62 

1O7 

46.34 

74-07 

235 

101.79 

209 

295' 

44 

1905 

108 

46.78 

172 

7450 

236 

102  23 

300 

2995 

^ 

1949 

109 

4721 

173 

74-94 

237 

102,66 

310 

34-2* 

46 

1992 

110 

?74 

75-37 

238 

10309 

320 

3862 

47 

20.35 

III 

48  08 

175 

75.80 

239 

103  53 

330 

42-95 

48 

20.79 

112 

48.51 

176 

76.23 

240 

103.96 

340 

47.23 

49 

21   22 

113 

48.94 

7667 

24I 

104.39 

51.61 

5i 

21.65 
22.O9 

"s 

4938 
4981 

!?9 

77  10 
77-53 

242 
243 

104.83 
105.26 

370 

55-94 
60.27 

52 

22.52 

116 

5024 

180 

77-97 

244 

105.69 

380 

64.61 

53 

22.95 

117 

5068 

181 

78.40 

245 

106.13 

390 

68.94 

54 

23-39 

nS 

5i  ii 

182- 

78.84 

246 

106.56 

400 

73  27 

P 

23.82 
24.26 

119 

12O 

51-54 
51-98 

183 
184 

79.27 
7970 

2-J7 
248 

106.99 
107.43 

500 
600 

21658 
259-90 

57 

2469 

121 

52.41 

185 

80.14 

249 

107.86 

7ix> 

30322 

58 

25.12 

122 

52.84 

1  86 

80.57 

250 

108.29 

800 

346.  54 

59 

25.55      | 

123 

53^28 

187 

81.00 

25' 

108.73 

yoo 

389.06 

00 

25-99  ; 

124 

53-71 

iS>i 

S..43 

252 

109.16 

10OO 

433  »8 

61 
62 

2642 
26.85  ! 

r* 

54-  '5 

5458 

189 
190 

81.87 
82.36 

253 

254 

1  1  o.  03 

63 

27.29  i 

127 

55-01    . 

x>r 

8273 

255 

110.46 

1 

64 

2772  i 

128 

55-44    « 

192 

83-»7 

256 

no  So 

From  catalogue  of  Chapman  Valve  Mfg.  Co. 
lo  nnd  the  pressure  per  sq.  in.  of  a  column  of  water  of  any  height  multi- 
ply the  height  of  the  column  by  .43318  (or  434,  as  it  is  usually  given.) 
See  note  on  next  page. 


Note,  as  to  table  on  last  page.  Many  suppose  that  a  well 
having  a  static  pressure  of  a  certain  number  of  pounds  per 
sq.  in.  has  the  same  service,  duty  and  volume  of  delivery  as 
would  be  obtained  from  a  column  of  water  falling  through  a 
pipe  of  same  size  and  with  a  head  corresponding  to  the  pres- 
sure of  the  well.  Such  is  not  the  case,  however,  there  being 
no  known  relationship  between  the  two  so  far  as  a  well  is 
concerned. 

To  illustrate— From  table  we  see  that  a  head  of  231  feet 
will  uive  a  pressure  of  100.08  pounds  per  square  inch  and 
(although  not  given  in  the  table)  a  certain  volume  will  be 
delivered  per  minute.  If  either  the  head,  pressure  or  vol- 
ume be  known  the  other  two  may  be  accurately  estimated. 
In  case  of  a  well,  however,  this  is  not  true.  A  well  having 
a  pressure  of  50  pounds  per  sq.  in.  may  throw  more  water 
than  another  well  having  a  pressure  of  100  pounds  per  sq. 
inch  and  either  one  may  throw  either  more  or  less  than  would 
be  delivered  from  a  pipe  of  the  same  size  having  a  head  of 
116  feet,  which  corresponds  nearly  with  a  pressure  of  50 
pounds  to  the  inch.  In  other  words— the  volume  of  a  well 
cannot  be  found  by  knowing  its  pressure;  nor  can  the  pres- 
sure be  found  by  knowing  its  volume.  The  pressure  must 
be  measured  with  a  gauge  and  the  volume  by  weiring  the 
stream  or  by  some  other  accepted  method. 

EVERY  WELL  SHOULD  BE  PBOVIDED 

WITH  A  GAUGE 

and  a  proper  record  preserved  of  the  pressures  during  differ- 
ent seasons  of  the  year,  during  different  stages  of  the 
weather  and  directions  of  the  wind  and  during  the  several 
stages  of  service  of  the  well. 

Systematic  records  thus  kept  would  no  doubt  go  far 
toward  settling  the  questions  of  source  and  supply.  It  has 
been  claimed,  and  apparently  on  good  grounds,  that  the 
standing  of  the  barometer  and  the  direction  of  the  wind  have 
a  marked  effect  on  both  the  volume  and  pressure  of  some 
wells.  No  systematic  records  having  been  kept  of  these 
observations  it  cannot  be  definitely  stated  that  the  fluctua- 
tions in  volume  and  pressure  of  the  wells  were  due  to  the 
changes  in  the  weather,but  the  matter  having  been  suggested 
is  one  well  worthy  of  attention  because  of  its  scientific  pos- 
sibilities. 

TABLE  NO.  25. 


Diam.  of 
pipe  in 
inches. 

Area  in 
square 
feet. 

Area  in 
square 
inches. 

Gals,     in 
900  feet 
of  pipe. 

Weight    of 
water   in 
900  feet. 

3 
4 
4.5 

5 
6 

7 
8 

.0491 
.0873 
.1105 
.1364 
.1963 
.2673 
.3490 

7.07 
12.56 

15.90 
19.64 

28.27 
38.48 
50.27 

330 

587 
743 
918 
1322 
1799 
2350 

2756  Ibs. 
4897    * 
6199    < 
7656    * 
11021    * 
15011    ' 
19598    « 

An  idea  may  be 
gained  from  this  ta- 
ble as  to  the  stupend- 
ous energy  necessary 
to  throw  out  this  vol- 
ume of  water  at  velo- 
cities ranging  from 
500  ft.  to  2000  feet  per 
minute  as  is  done  by 
Dakota's  Artesian 
Wells. 


TABLE  NO.  26. 
From  Trautwine's  "Civil  Engineer**  Pocket  Book/' 


CONTENTS  OF  CYLINDERS,  OR  PIPES. 


Contents  for  one  foot  in  length,  in  Cub  Ft,  and  in  U.  S.  Gallons  of 

231  cub  ins,  or  7.4805  Galls  to  a  Cub  Ft.    A  cub  ft  of  water  weighs  about  62^  Ibs  ;  and  a  gallon 
about  8^  Ibs.    Diams  2,  8,  or  1O  times  as  great,  give  4,  9,  or  100  t'~-~  »v"  Content. 

For  the  weight  of  water  in  pipes,  see  Table   No. 22 


For  1ft.  in 

For  1  ft  in 

For  1  ft.  ia 

length. 

length. 

leu 

gth. 

Diam. 

Diam. 

Diam. 

Diam. 

Diam. 

in 

in  deci- 

. a 

*-.    CO 

in  deci- 

^ S 

fc.    OS 

Diam. 

in  deci-     _^.o 

-    CO 

IDS. 

mals  of 

"S'JJ 

°  >9 

IBB. 

mals  of 

'S'^ 

°  >2 

in 

malsof     IJ'ja   . 

o  a 

a  foot. 

EC,  ££ 

la" 

a  foot. 

fc  *£ 

N 

Ins. 

a  foot.  (  &.  £}  C 

a  £ 

•go  g1 

!<§ 

lj* 

=  0 

^ 

|o 

oq 

°s 

5»*« 

Oi 

^ 

°i 

J4 

.0208 

.0003 

.0025 

y 

.5625 

.2485 

1.859 

19. 

1.583 

1.969 

14.73 

5-16 

.0260 

.0005 

.0040 

1. 

.5833 

.2673 

1.999 

72 

1.625 

2.074 

15.51 

78 

.0313 

.0008 

.0057 

\/ 

.6042 

.2867 

2.145 

20. 

1.667 

2.182 

16.32 

7-16 

.0365 

.0010 

.0078 

•U    .6250 

.3068 

2.295 

K 

1.708 

2.292 

17.15 

\/ 

.0417 

.0014 

.0102 

74 

.6458 

.3276 

2.450 

21 

1.750 

2.405 

17.99 

9-16 

.0469 

.0017 

.0129 

8. 

.6667 

.3491 

2.611 

72 

1.792 

2.521 

18.86 

7ft 

.0521 

.0021 

.0159 

i^    .6875 

.3712 

2.777 

22. 

1.833 

2.640 

19.75 

11-16 

.0573 

.0026 

.0193 

i|    .7083 

.3941 

2.948 

72 

1.875 

2.761 

20.66 

3£ 

.0625 

.0031 

.0230 

%   .7292 

.4176 

3.125 

23. 

1.917 

2.885 

21.58 

13-16 

.0677 

.0036 

.0269 

9.       .7500 

.4418 

3.305 

Yz    1.958 

3.012 

22.53 

is 

.0729 

.0042 

.0312 

Til  -7708 

.4667 

3.491 

24.       2.000 

3.142 

23.50 

15-16 

.0781 

.0048 

.0359 

i|    .7917 

.4922 

3.682 

25. 

2.083 

3.409 

25.50 

1. 

.0833 

.0055 

.0408 

%    .8125 

.5185 

3.879 

26. 

2.167 

3.687 

27.58 

\/ 

.1042 

.0085 

.0638 

10. 

.8333 

.5454 

4.080 

27. 

2.250 

3.976 

29.74 

72 

.1250 

.0123 

.0918 

YA    .8542 

.5730 

4.286 

28. 

2.333 

4.276 

31.99 

74 

.1458 

.0167 

.1249 

i|   .8750 

.6013 

4.498 

29. 

2.417      4.587 

34.31 

2.      ' 

.1667 

.0218 

.1632 

%   .8958 

.6303 

4.715 

30. 

2.500      4.909 

36.72 

/4 

.1875 

.0276 

.2066 

11. 

.9167 

.6600 

4.937 

31. 

2.583      5.241 

39.21 

72 

.2083 

.0341 

.2550 

i^i  .9375 

.6903 

5.164 

32. 

2.667      5585 

41.78 

74 

.2292 

.0412 

.3085 

i|   .9583 

.7213 

5.S96 

33. 

2.750      5.940 

44.43 

3. 

.2500 

.0491 

.3672 

%   .9792 

.7530 

5.633 

34. 

2.833  i   6.305 

47.13 

/4 

.2708 

.0576 

.4309 

12.     1  Foot. 

.7854 

5.875 

35. 

2.917      6.681 

49.98 

\/ 

.2917  I  .0668 

.4998 

34L042 

.8522 

6.375 

36. 

3000      7.069 

52.88 

74 

.3125      .0767 

.5738 

13.     !l.083 

.9218 

6.895 

37. 

3.083  I  7.467 

55.86 

4. 

.3333 

.0873 

.6528 

14L125 

.9940 

7.436 

38. 

3.167 

7.876 

58.92 

74 

.3542 

.0985 

.7369 

14.      1.167      1.069 

7.997 

39. 

3.250 

8.296 

62.06 

72 

.3750 

.1104 

.8263 

1^1.208     1.147 

8.578 

40. 

3.333     8.727 

65.28 

74 

.3958 

.1231 

.9206 

15.     1.250     1.227 

9.180 

41. 

3.417     9.168 

68.58 

5. 

.4167 

.1364     1.020 

M1.292     i  1.310 

9.801 

42. 

3.500  !  9.621 

71.97 

/4 

.4375 

.1503     1.125 

16.      1.333      1.396     10.44 

43. 

3.583 

10.085 

75.44 

72 

.4583 

.1650 

1.234 

141.375      1.485      11.11 

44. 

3.667 

10.559 

78.99 

74 

.4792 

.1803 

1.349 

17.      1.417     !l.576     11.79 

45. 

3.750    11.045 

82.62 

6.     ' 

.5000 

.1963 

1.469 

141.458      1.670     !l2.49 

46. 

3.833  ill.  541 

86.33 

& 

.5208 

.2131 

1.594 

18.     1.500     1.767      13.22 

47. 

3.917    12.048 

90.13 

.5417 

.2304 

1.724 

141.542     1.867 

13.96 

48. 

4.000    12.566 

94.00 

\ 

Table  continued,  but  with  the  diams  in  feet. 


Diam. 
Feet. 

Cub. 
Feet. 

U.  s. 

Galls. 

Diam. 
Feet. 

Cub. 
Feet. 

U.  S. 
Galls. 

Dia.  \    Cub. 

Feet.1    Feet. 

U.  S. 
Galls. 

Dia. 
Feet. 

Cub. 
Feet. 

U.S. 
Galls. 

4 

12.57 

94.0 

7 

38.49 

287.9 

12  !   113.1 

846.1 

24 

452.4 

3384 

1^ 

14.19 

106.1 

^ 

41.28 

308.8 

13      132.7 

992.8 

25 

490.9 

3672 

X^ 

15.90 

119.0 

i^ 

44.18 

330.5 

14      153.9 

1152. 

26 

530.9 

3971 

74 

17.72 

132.5 

74 

47.17 

352.9 

15      176.7 

1322. 

27 

572.6 

4283 

5 

19.64 

146.9 

8 

50.27 

376.0 

16      201.1 

1504. 

28 

615.8 

4606 

\A 

21.65 

161.9 

M 

56.75 

424.5 

17  i  227.0 

1698. 

29 

660.5 

4941 

/•£ 

23.76 

177.7 

9 

63.62 

475.9 

18      254.5 

1904. 

30 

706.9 

5288 

74 

25.97 

194.3 

M 

70.88 

530.2 

19      283.5 

2121. 

31 

754.8 

5646 

6 

28.27 

211.5 

10 

78.54 

587.6 

20      314.2 

2350. 

32 

804.3 

0017 

5* 

30.68 

229.5 

J-2 

86.59 

647.7 

21      346.4   j  2591. 

33 

855.3 

6398 

B 

33.18 

248.2 

11 

95.03 

710.9 

22      380.1       2844. 

o4 

907.9 

6792 

i 

35.79 

267.7 

Ji 

103.90 

777.0 

2:-!      415.5       3108. 

35      962.1 

7197 

67  fy^ 

TABLE  NO.  27/ 

RELATIVE   DISCHARGING  CAPA€^jfeK»-O^  FULL 
SMOOTH  PIPES. 


Dia. 
in 
Feet. 

Relative 
Discharg'g 
Power. 

3 

4 

6 

8 

10 

12 

14 

16 

=  « 

-    ** 
II 

Q~ 

48 
44 
40 
36 
33 
3° 
27 
24 

22 
2C 

18 
16 
M 

12 

10 

8 
6 
4 
3 

d 

4- 
3.667 

3-333 
3- 
2.750 
2.500 
2.250 

48 

1.667 

1.500 

1-333 
1.167 

\3 
.667 

.500 

•333 
.250 

31 

32.0OO 
25750 

S» 

12.S4I 
9.859 

7-594 
5-657 

2.756 

2-052 

1471 
I. 

.6339 
.3629 
.1768 
.0641 
.0312 

15-59 
12.54 
9.85 

7-59 
6.ii 
,  4-8o 
3-70 
2-75 
2.16 
1.74 

1-34 
i 

17-5° 
13-47 
8.41 
8.52 

6-54 
5.16 
3-84 
309 
2-43 
1.87 

1-39 
i 

20.27 

I5-58 
12.54 
9.85 
7.59 
5-65 

4-5> 
3.58 

2-75 
2.05 
1.47 
i 

34-55 
27.09 
16.61 
1558 

12.53 
9.88 

7-J5 
5.65 
4.05 
2.75 

1-74 
i 

19.78 

15-54 
996 
8.92 

7-<7 
5.66 

4-34 
3-23 
2.32 

1-57 
I 

42.95 
32.00 

25.73 
20.29 

15.58 

1  1.  So 

8.52 

s-65 
3-58 
2.05 
i 



70.96 
55.96 
42.01 
32.01 
22.94 
15.60 
9.88 
5-66 

2-75 
i 

65-77 
47.14 
32-05 
20.31 
11.63 
5-66 
2.05 
I* 

i 

From  ].  T.  FANNING^  "Water  Supply  Engineering.0 

The  foregoing  table  shows  approximately  the  relative  discharging  pow- 
ers of  pipes  of  different  diameters.  In  the  second  colnmn  the  diameter  1 
foot  is  assumed  as  a  unit,  and  the  figures  show  the  relative  discharging 
value  of  pipes  whose  diameter  is  given  in  the  first  column ;  for  example,  a 
pipe  four  feet  in  diameter  will  discharge  32  times  as  much  water  as  one 
which  is  one  foot  in  diameter,  other  things  being  equal ;  a  pipe  3  feet  in 
diameter  15.588  times  as  much,  one  2£  feet  in  diameter,  9.859  times  as  much 
and  so  on. 

*•  The  numbers  at  the  intersections  of  the  horizontal  and  vertical  columns 
from  the  diameters  in  inches  give  also  approximate  relative  discharging 
capacities.  For  example,  a  48-inch  pipe  is  equal  to  15.59, 16-inch  pipes,  or 
we  find  that  a  24-inch  pipe  is  equal  to  32,  6-inch  pipes  or  15.58,  8-inch  pipes, 
and  that  a  12-inch  pipe  is  equal  to  5.65,  6-inch  pipes. 


68 

TABLE  NO.  28. 
FRICTION  HEADS  AND  DISCHARGES. 

For  100  feet  of  pipe.       By  Wiesbach's  Formula.  Trautwine. 


Diam.  in  Inches. 

Vel.  in 

Vel- 

( 

Feet 

head  in 

o 

«*/2 

4 

4^ 

5 

t«rSec 

Feet. 

Frhead 

Ft  per 
100  ft. 

Cub  ft 
per  Mir 

Frhead 
Ft  per 
100  ft. 

Cub  ft 
per  Mir 

Frhead 
Ft  per 
100  ft. 

Cub  ft 
per  Min 

lOoTJ   Per  Mit 

Frhead 
Ft  per 
100ft. 

Cub  ft 
per  Mia 

2.0 

.062 

.659 

5.89 

.565 

8.02 

.494 

10.4 

.439 

13.2 

.395 

16.3 

2.2 

.075 

.780 

6.48 

.669 

8.82 

.585 

11.5 

.520 

14.6 

.463 

18.0 

2.4 

.090 

.911 

7.07 

.781 

9.62 

.683 

12.5 

.607 

15.9 

.547 

19.6 

2.6 

.105 

1.05 

7.65 

.901 

10.4 

.788 

13.6 

.701 

17.2 

.631 

21.3 

2.8 

.122 

1.20 

8.24 

1.03 

11.2 

.900 

14.6 

.800 

18.5 

.720 

22.9 

3.0 

.140 

1.35 

8.83 

1.16 

12.0 

1.02 

15.7 

.905 

19.8 

.815 

24.5 

3.2 

.160 

1.52 

9.42 

1.31 

12.8 

1.14 

16.7 

1.02 

21.2 

.915 

26.2 

3.4 

.180 

1.70 

10.0 

1.46 

13.6 

1.27 

178 

1.13 

22.5 

1.02 

27.8 

3.6 

.202 

1.89 

10.6 

1.62 

14.4 

1.41 

18.8 

1.26 

1.13 

29.4 

3.8 

.225 

2.08 

11.2 

1.78 

15.2 

1.56 

19.9 

1.39 

25/2 

1.25 

31.0 

4.0 

.250 

2.28 

11.8 

1.96 

16.0 

1.71 

20.9 

1  .52 

20.5 

1.37 

32.7 

4.2 

.275 

2.49       123 

2.14 

16.8 

1.87 

22.0 

1.66 

27.8 

1.50 

34.3 

4.4 

.302 

2.71       12.9 

2.33 

176 

2.03 

23.0 

1.81 

29.1 

1.63 

36.0 

4.6 

.330 

2.94    j  13.5 

2.52 

18.4 

2.21 

24.0 

1.96 

304 

1.76 

37.6 

4.8 

.360 

3.18    ;  14.1 

2.72 

19.2 

2.38 

25.1 

2.12 

31.8 

1.91 

39.2 

5.0 

.390 

3.43       14.7 

2.94 

20.0 

2.57 

26.2 

2.28 

33.1 

2.05 

40.9 

5.2 

.422 

368       15.3 

3.15 

20.8 

2.76 

27.2 

2.45 

34.4 

2.21 

42.5 

5.4 

.455 

3.94       15.9 

3.38 

21.6 

2.96 

28.2 

2.63 

35.8 

2.37 

44.2 

5.6 

.490 

4.22    j  16.5 

3.61 

22.4 

3.16 

29.3 

2.81 

37.1 

253 

45.8 

5.8 

.525 

4.50       17.1 

3.85 

23.2 

3.37 

30.3 

3.00 

38.4 

2.70 

47.4 

6.0 

.562 

4.78    !  17.7 

4.10 

24.0 

3.59 

31.4 

3.19 

39.7 

•2.87 

49.1 

6.2 

.600 

5.08       18.2 

4.36 

24.8 

3.81 

32.4 

3.39 

41.0 

3.05 

50.7 

6.4 

.640 

5.39       18.8 

4.62 

25.6 

4.04 

33.5 

3.59 

42.4 

3.23 

52.3 

6.6 

.680 

5.70    ;  19.4 

4.89       26.4 

4.28 

34.5 

3.80 

43.7 

.3.42 

54.0 

6.8 

.722 

0.02       20.0 

5.16    i  27.3 

4.52 

35.6 

4.01 

45.0 

3  61       55.6 

7.0 

.765 

635       20.6 

5.45       L8.0 

4.77 

36.6 

4.24 

464 

3.81    |  57-2 

Diam.  in  Inches. 

Vel.  in 
Feet 

Vel- 
head  in 

6 

7 

8 

9 

10 

per  Sec. 

Feet. 

KSSortn 

KjperMin 

Frhead 
Ft  per 
100  ft. 

Cub  ft 
per  Min 

Frhead 
Ft  per 
100ft. 

Cub  ft 
per  Min 

FFjrth,?^i   Cub  ft 

i&fft.  per-Mi<> 

afteft 

2.0 

.062 

.329 

23.5 

.282 

32.0 

.247 

41.9 

.220 

53.0 

.198  1     65.4 

2.2 

.075 

.390 

25.9 

.334 

35.3 

.293 

46.1 

.260 

58.3 

.234 

72.0 

2.4 

.090 

.456 

28.2 

.390 

38.5 

.342 

50.2 

.304 

63.6 

.273 

78.5 

2.6 

.105 

.526 

30.6 

.450 

41.7 

.394 

54.4 

.350 

68.9 

.315 

85.1 

2.8 

.122 

.600 

32.9 

.514 

449 

.450 

58.6 

.400 

74.2 

.360 

91.6 

3.0 

.140 

.679 

35.3 

.582 

48.1 

.509 

62.8 

.453 

79.5 

.407 

98.2 

3.2 

.160 

.763 

37.7 

.054 

51.3 

.572 

67.0 

.508 

84.8 

.458 

105 

3.4 

.180 

.851 

400 

.729 

54.5 

.638 

71.2 

.567 

90.1 

.510 

111 

3.6 

.202 

.943 

42.4 

.808 

57.7 

.707 

75.4 

.629 

95.4 

.565 

118 

3.8 

.225 

1.04 

44.7 

.892 

60.9 

.780 

79.0 

'.693 

101 

.624 

124 

4.0 

.250 

1.14 

47.1 

.979 

64.1 

.856 

83.7 

.761 

106 

.685 

131 

4.2 

.275 

1.25 

49.5 

.07 

67.3 

.935       87.9 

.832 

111 

.748 

137 

4.4 

.302 

1.35 

51.8 

1.10 

70.5 

1.02 

92.1 

.905 

116 

.814 

144 

4.6 

.330 

1.47 

54.1 

1.26 

73.7 

1.10 

96.3 

.981 

122 

.883 

150 

4.8 

.360 

1.59 

56.5 

1.36 

76.9 

1.19 

100 

1.06 

127 

.954 

157 

5.0 

.390 

1.71 

58.9 

1.47 

80.2 

1.28 

105 

1.14 

132 

1.03 

163 

5.2 

.422 

184 

61.2 

1.58 

83.3 

1.38 

109 

1.23 

138 

1.10 

170 

5.4 

.455 

1.97 

63.6 

1.69 

86.6 

1.48 

113 

1.31 

143 

1.18 

177 

5.6 

.490 

2.11 

65.9 

1.81 

89.8 

1.58 

117 

1.40 

148 

1.26 

183 

5.8 

.525 

2.25 

68.3 

1.93 

93.0 

1.68 

121 

150 

154 

1.35 

190 

6.0 

.562 

2.39 

70.7 

205 

96.2 

1.79 

125 

1.59 

159 

1.43 

196 

6.2 

.600 

2.54 

73.0 

2.18 

99.4 

1.90 

130 

1.69 

164 

1.52 

203 

6.4 

.640 

2.69 

75.4 

2.31  <- 

102 

2.02 

134 

1.79 

169 

1.61 

209 

6.6 

.680 

2.85 

77.7 

2.44 

106 

2.14 

138 

1.90 

175 

1.71 

216 

6.8 

.722 

3.01 

80.1 

2.58 

109 

2.26 

142 

2.01 

180 

1.81 

222 

7.0 

.765 

3.18 

82.4 

2.72 

112 

2.38 

146 

2.12 

185 

1.90 

229 

See  exmaple  of  use  on  page  69. 

69 

Example  of  use  of  table  No.  28.  I  have  150  Ibs.  pressure 
at  well;  2000  ft.  of  3  inch  pipe  discharging  110  gallons  per 
minute.  What  is  the  effective  pressure  at  point  of  discharge  ? 
From  table  36  we  find  that  110  gals.  =  14.7  cu,  ft.  From  ta- 
ble 28,  under  head  of  3  inch  pipe,  we  find  14.7  cu.  ft.  discharge 
=  5  ft.  velocity  per  sec.  and  a  loss  of  3.43  ft.  head  per  100  ft. 
3.43  X  20  =  68.6  =  ft.  loss  of  head  in  2000  ft.  of  pipe.  From 
table  24  we  find  68.6  ft.  head  to  =  29.7  Ibs.  of  pressure.  150 
Ibs.  (given  pressure)— 29.7  Ibs.—  120.3  lbs.=  effective  pressure 
at  point  of  discharge. 

Further  example  of  use  of  tarble  28. 

To  get  discharge  from  pipe  of  given  size  and  length. 

From  table  28— within  certain  limits  —may  be  found  the 
volume  discharged  by  a  pipe  of  given  size  and  length,  under 
a  given  pressure. 

Example:  A  well  has  a  pressure  of  78  Ibs.  per  inch,  and  it 
is  desired  to  convey  water  to  a  reservoir  through  3000  ft.  of 
3  inch  pipe;  what  will  the  pipe  discharge  per  minute  at  the 
reservoir?  From  table  24  (P.  64.)  we  find  that  78  Ibs.  =  head 
of  180  ft.  which  head  is  to  be  used  to  force  the  water  through 
30  hundred  feet  of  pipe,  therefore  ^  of  180  =  6  ft.  =  the 
available  head  for  100  it.  In  table  28  we  find,  under  3  inch 
pipe,  the  nearest  corresponding  friction  head  which  is  6  02 
ft.  which  corresponds  to  a  velocity  of  6.8  ft.  per  sec.  and  a 
volume  of  20  cubic  ft.  per  minute,  which,  from  table  36  = 
149.6  gallons.  (No  account  is  here  taken  of  the  velocity  head 
which  is  less  than  1  ft.  and  remains  the  same  for  any  length 
of  pipe;  being  dependent  only  upon  the  velocity  in  the  pipe.) 

Over  column  two  of  table  No.  28  appears  the  heading 
"  Vel.  head  in  ft.",  and  over  column  three  appears  the  head- 
ing "  Fr.  head  ft.  per  100  ft."  The  first  is  read  as  Velocity 
head  and  the  second  as  Friction  head.  The  distinction  is 
here  explained. 

By  Head  is  meant  the  vertical  distance  in  feet  between  the  surface  of 
the  source  of  supply  and  the  centre  of  the  orifice  through  which  the  water 
flows.  The  total  head  is  divided  into  3  parts  called,  respectively,  Entry 
Head-  Velocity  Head,  and  Friction  Head ;  the  respective  func- 
tions of  which  are  as  follows : 

Entry  Head  is  that  portion  of  the  total  head  used  in  overcoming  the 
resistance  to  the  entry  of  the  water  into  the  pipe.  The  entry  head  is  less 
as  the  edges  at  the  point  of  entry  are  rounded.  It  is  equal  to  about  one- 
half  the  velocity  head. 

Velocity  Head  is  that  portion  of  the  total  head  used  in  maintaining 
a  certain  velocity  within  the  pipe,  assuming  that  there  is  no  friction  m  the 
pipe.  It  is  therefore  equal  to  the  height  through  which  a  body  would  fall 
— in  a  vacuum — to  gain  the  same  velocity  as  that  of  the  water  in  the  pipe. 

V2 
Expressed  as  a  formula  Vel.  Hd.  =  -^-  ,  in  which   V2 

the  square  of  the  velocity  in  ft.  per  sec.  and  g  =  the  acceler- 
ation  of   gravity,    or  32.2.       The  formula  then  becomes 

V2 

Velocity    Head  =-^j  •  or,  what  is  practically  the  same- 
Velocity  or       )  _  (  square  of  vel.  >  v  m  -  ~ 
Theoretical  Head  J  ~  { in  ft.  per  sec.  J  * 

The  velocity  head  rarely  exceeds  1  ft.  and  is  constant  for  all  lengths  of  pipe. 


70 

Friction  Head  is  the  remainder  of  the  total  head;  or  such 
an  amount  as  is  just  sufficient  to  overcome  the  friction  in 
the  pipe  leaving  the  remaining  head  to  cause  the  entry  and 
velocity  of  the  flow.  The  smoother  and  shorter  the  pipe  is 
the  less  the  friction  head  will  be  and  the  greater  the  velocity 
head  will  become. 

The  Theoretical  Velocity  due  to  any  given  head  is,  if  ex- 
pressed in  a  formula— 


=  \2gh  =   <64.4h,   in  which  h  =  the  gh 

head  in  feet. 

This  is  practically  the  same  as  Theor.  Vel.  =  8.03  times 
the  sq.  rt.  of  h. 

Example— What  is_the  theoretical  vel.  under  a  head  of  4 
ft?  v'64.4  X  4  =  \25~T6  which,  from  table  of  roots,  =  16.05— 
or— by  the  second  rule,  the  sq.  rt.  of  h  (4  ft.)  =  2  which  X 
8.03  =  16.06. 

e 

The  above  explanation  will  not  only  explain  clearly  the 
significance  of   the  values  in  table  28  but  will  also  be  of  us 
otherwise. 

Table  29  is  similar  to  table  28,  except  that  the  velocities  in 
the  pipe  are  in  single  feet,  and  extend  to  20  feet,  instead  of 
in  feet  and  decimals,  as  in  table  28.  The  values  in  table  29 
differ  slightly  from  those  clue  to  corresponding  sizes  and  vel- 
ocities given  in  table  28.  This  difference  is  due  to  calcula- 
tions having  been  made  from  different  formulae,  but  they 
are  too  slight  to  be  material  since  the  variations  in  the  pipes 
themselves  will  cause  as  great  variations— either  more  or  less 
— from  the  quantities  given  in  either  table. 

The  limits  of  tables  28  and  29  are  too  narrow  to  suit  all  the 
conditions  of  our  wells  and  practice,  so  a  few  simple  rules 
are  given  to  suit  all  conditions,  these  rules,  and  table  30  upon 
which  they  are  based,  being  adapted  from  Haswell's  Pocket 
Book. 

It  may  be  added  that  by  reason  of  varying  conditions 
whatever  rules  or  formulae  are  applied  the  result  will  be 
in  a  measure  approximate. 

To  find  the  Friction  Head. — Wiesbach's  Formula. 

.01716      )      Length        Vel2  in 
Friction  head     )    ^144  _j_     i        .     „ :  (       in  feet      ft  per  sec 

in  feet        =   )  f  X  Diam    >        64.4 

>J  per  sec     J       jn   feet 

The  use  of  this  formula  requires  a  knowledge  of  the  velo- 
city in  ft.  per  sec.  which  may  be  found  by  dividing  the  vol- 
ume in  cubic  ft.  per  second  by  the  area  of  the  pipe.  (See 
page  82.) 


TABLE  NO.   2>i). 

I*OSS  OP  HEAD  BY  FRICTION  OF  WATER  IN 

CALCULATED  FOR  PIPES  1OO  FEET  LONG. 


Velocity 
of 
Water 

through 
Pipe  in 
Feet  per 

Second. 

INSIDE    DIAMETER    OF    FIFE    IN    INCHES. 

3 

4 

5 

6 

7 

8 

Discharge  per  Min. 
in  Cubic  Feet  

sf 

o-o 

o.-*» 
c  ^ 

k 

I'll 

Discharge  per  Min. 
in  Cubic  Feet  

No.  of  Ft.  Loss,  ofl 
head  due  to  friction' 

i 

n  n 

fa 

I    2 
•   5' 

No.  of  Ft.  Loss  of 
head  due  to  friction 

rtf 
ST 

cr  SJ 
n'1* 
•»1 

51 

i  r 

!   3 

if 

eLo 

0."** 

s? 

o 

?8 
I's, 

Discharge  per  Min. 
in  Cubic  Feet  

No.  of  Ft.  Loss  of 
head  due  to  friction] 

Discharge  per  Min. 
in  Cubic  Feet  

No.  of  Ft.  Loss  ofl 
head  due  to  friction] 

1 

2.95 

.196 

5.22 

.147 

8.17 

.118 

11.77 
23.54 

.098 

16.03 

.084 

20.88 

.074 

2 

5.89 

•659 
1.35 

10.44;  -494 

16.34 

•395 

.329 

32-05 

.282 

4X-76 

.247 

3 

8.83 

15-67 

1.02 
I.7I 

24.51 

.815 

35.32 

.679 

48.08 

.581 

6264 

•509 

4 

11.80 

2.28 

20.89 

32.69 

1.37 

47.09 

58.87 

1.14 

64.11 

•977 

83.52 

.856 

5 

1 
14.70 

17.70 

3-43 

26  12    2.57 

40.87 

2.05 

1.71 

80.15 

1-47 

104.40 

1.28 

6 

4.78 

31-34 

3-59 

49-05 

287 

70.64 

2.39 

96.18 

2.05 

125.28 

1.79 

7 

20.60   6.35 

36.57 

4-77 

57.22 

3-8. 

82.41 

3-18 

112.  21 

2.73 

146.16 

2.39 

8 

23.56 

8.14 

41-79 

6.H 

65.40 

4.89 

94.19 

4.07 

Jf? 
6.16 

128.24 

3-49 

167.04 

3.06 

9 

26.51 

10.12 
12.32 

47-02 

7-59 

73.57 

6.07 
739 

10597 

144.27 

434 
5.28 

187.92 
208.80 

3-79 

10     | 

J9-45 
32.40 

52.24 

9-24 

81-75 

117.74 

160.30 

4.62 

11 

M.7, 

57-47 

11.03 

89.92 
98.10 

8.82 

12952 

7-36 

I7€.34 

6.31 

229.68 

5.52 

12 

35-34 

17.31 

62.70 

12.98 
15.08 

10.38 

141.30 

8.65 

*92  37 

7-4J 

250.56 

6.49 

13 

38.33 

20.10 
23.12 

67.92 

106.27 

12  06 

153.07 

10.05 

208  40 

8.61 
9.91 

271.44 

7-54 

14 

4123 

73-15 

17.34 

"4-45 

13.87 

164.85 

11.56 

224.43 

292.32 

8.67 

15 

44.20 
47.12 

26.32 

78.38 

19-74 

122.62 

1579 

17663 

13.16 

240.46 

11.28 

313.20 

9.87 

16 

29.7*, 

>   83.60 

22  29 

130.80 

17.83 

188.40 

14.86 

256.48 

12.74 

334.o8 

11.15 

17 

50-05 

33-33 

88.8325.00 

138.97 

20.00 

200.18 

16.67 

272.51 

14.29 

35496 

12.50 

18 

53.00 

37-14 

94.05 

27.86 

147.15 

22.29 

211.96 

18.57 

288.54 

5-92 

375.84 

3-93 

19 

5595 

4M2 

99.28 

30.84     155.32*24.67 

223.73 

2056 

304.57 

7.62 

396.73 

5.43 

20 

58.89 

45-32 

104.50 

33-99   »«3-5°  *7  19 

235.51 

23.66 

330.60 

9.42 

417.60117.00 

72 
TABLE  SO.  30. 


TABLE  AND  RULES. 


From  Ha. -*>'•?! I. 


ter  T«tai-  ™  i 

Diameter 
inches. 

Tabular 

No. 

1                           4.71 

7 

612 

32 

1*4                                       S-^ 

854 

99 

m  '             13.02 

9 

1147 

61 

i^it               19  i~> 

10 

1493 

5 

2                           26  .'69 

11 

1894 

9 

2.',                          4H.t)7 

12 

2356.0 

3"                          73.  :> 

13 

2876 

7 

3i                        108.14 

14 

3463 

3 

4                         151.02 

lo 

4115 

9 

4J                       194.84 

16 

4836 

9 

r>                         263.87 

17 

562S 

5 

6             1            416.54 

18 

!            6493 

1 

APPLICATION  OF  THE  TABLE. 

I.    To  Compute  Volume  Discharged—  Length  of  Pipe,  Diam- 
eter, and  Fall  or  Head  being;  given. 

RULE—  Divide  the  tabular  number,  opposite  to  the  diameter  of  the  pipe. 
by  the  square  root  of  the  rate  of  inclination  (head),  and  the  quotient  will 
give  the  volume  required  in  cu.  ft.  per  min. 

EXAMPLE—  A  pipe  has  a  diameter  of  4  inches,  a  length  of  2982  ft.  and  a 
head  of  123  pounds  pressure  (284  ft.)  What  is  the  discharge  per  min.? 

=N  10.5=3.  24,  and  tabular  number  for  4  in.  =  151.02. 


J?^? 
284 


then,  !|!A-=46.6  cu.  ft.  per  min.=(from  table  36)  119  68  gals 

If  head,  as  in  above  case,  is  iupoimds  pressure  reduce  it  to 
feet  by  reference  to  table  24;  but  if  pipe  is  not  connected 
with  the  well,  and  the  pressure  is  due  to  gravity  alone,  then 
the  head  will  be  the  vertical  distance  between  the  upper  and 
the  lower  ends  of  the  pipe.  Keduce  volume  in  cubic  feet  to 
volume  in  gallons  by  reference  to  table  36. 

II.  To  compute    the  Diameter  necessary  to   discharge   a 
given  Volume—  the  Head  and  Length  being  given. 

RULE—  Multiply  the  given  volume  by  the  square  root  of  the  ratio  of  the 
inclination—  head  —  ;  take  the  nearest  corresponding  number  in  the  table, 
and  opposite  to  it  is  the  diameter  required. 

EXAMPLE—  A  pipe  has  a  length  of  2982  feet,  the  head  is  123  Ibs.,  (284  ft.) 
What  size  of  pipe  will  it  require  to  discharge  46.6  cubic  feet  (119.68  gals.) 
per  minute?  _ 

/9QG9 

46.  6x   /^1=46.6x3,24=150.98.    The  nearest  tabular  num- 

N/    <s84 
ber=  151.02  opposite  which  is  4  inches  —  required  size. 

III.  To    compute    the   Head—  the    Length,  Diameter  and 
Volume  of  discharge  being  given. 


per  minute  through  the  pipe. 

EXAMPLE — WThat  head  in  ft.  (or  pressure  in  Ibs)  will  be  required  to  cause 
a  discharge  of  46.6  cu.  ft.  (119.68  gals.)  of  water  per  minute  from  2982  ft.  of 
4  in.  pipey 

^Ii5?=3.24;  3.242  =  10.5;  2982-^-10.5  =  284  ^required  head  in 
feet  which  =  123  Ibs.  pressure. 


78 

TABLK  NO.  31. 

HORIZONTAL   AND   VERTICAL   DISTANCES   REACHED   BY  JETS. 


PRESSURE  AT  NOZZLE. 

^Ojj 

5  o 

Head  in  Ibs.  per  sq  .  in.  .  . 

20 

30 

40 

50 

00 

70 

So 

90 

too 

~  ^ 

E9.VAL  - 

Head  in  feet  

46.2 

92  4 

'  '5-5 

138.6 

161  7 

184  8 

2O7  O 

*.<j. 

**•'  / 

"•"!•" 

*w/>y 

in 

1 

{Gallons  discharged  
Horizontal  distance  of  jet 

no 
70 

'34 
90 

'55 
109 

'73 

126 

189 
142 

205 
'56 

219 

1  68 

232 
178 

ft 

Vertical             "            «• 

43 

79 

94 

108 

121 

J3' 

140 

•'45 

1* 

{Gallons  discharged.  ..   . 

7' 

170 
93 

196 

2  19 

132 

240 
.48 

259 
'63 

277 
'75 

$ 

?W 

Hori/.ogtal  distance  of  jet 

Vertical 

43 

63 

I8i 

97 

112 

125 

'37 

148 

»S7 

1* 

{Gallons  discharged  
Horizontal  distance  of  jet 

171 
73 

210 
96 

242 
i.8 

271 

J97 

320 

•72 

iS 

363 
198 

207 

Vertical 

43 

63 

82 

99 

"S 

129 

142 

'54 

164 

^ 

(  Gallons  discharged  
<  Horizontal  distance  of  jet 

207 

75 

253 
1DO 

293 
124 

327 

146 

f§ 

3S7 
184 

4'3 

200 

439 

2l\ 

462 
224 

'  Vertical             '*            " 

44 

65 

85 

102 

1  18 

I46 

'58 

.69 

FROM  FAXNING'S  "WATER  SUPPLY". 


To  calculate  the  altitude  reached  by  jets. 


A=H  /HaX.Q125  j      (  in  which  A  =  altitude  required,  H  =  head  on  jet  in 
*     SXD      /      (  feet,  and  D  =  diameter  of  nozzle  in  inches, 

EXAMPLE—  What  will  be  the  altitude  of  a  jet  discharged  from  a  IVZ  inch 
nozzle  under  a  head  of  80  pounds  pressure? 

(The  head  being  given  in  Ibs.  reduce  it  to  feet  by  multiplying  by  2.311— 
1  pound  per  sq.  in.  equalling  2.311  ft.  of  head.) 

80  Ibs.  X  2.311  =  184.88  =  head  in  feet. 


Then  A  -  184.88-  1        =149.28  ft,  altitude. 


To  calculate  discharge  of  jets  in  gallons  per  minute. 


<-8Tk\2  N,  n  oww 
<  0.288 


in  which  G=discharge  in  gals,  per  min.  H  = 
{head  of  jet  in  ft.    D=diam.  of  nozzle  in  inches 


Using  above  example.    What  will  be  the  discharge  per  min.  from  a 
inch  nozzle  under  a  head  of  184.88  feet.    (=80  Ibs.  pressure) 


\'H  =v'184.88=13.597  and  (8  D)2  =  (8X1.5)2=144. 

Then  formula  becomes  G=13,597X  144x0.288  which=563.89  gallons  per 
minute.  In  this  way  the  volume  of  a  well  may  be  calculated  very  closely. 
Table  No.  38,  page  89  gives  the  discharges  from  different  nozzles,  under 
different  heads,  as  calculated  by  this  formula. 


SOURCE  AND  SUPPLY. 

"Where  does  the  artesian  water  come  from?"  has  been 
asked  a  thousand  times,  but  has,  as  yet,  received  no  answer, 
other  than  a  purely  theoretical  one.  Nor  can  any  answer 
be  given  until  a  careful  geological  survey  has  been  made  of 
this  state  and  those  adjoining  it;  and  until  some  systematic 
investigations  are  made  in  the  field  of  the  wells  themselves. 
When  more  wells  have  been  drilled,  so  that  the  influence  of 
one  upon  another  may  be  ascertained,  or  when  a  series  of 
purely  experimental  wells  shall  have  been  drilled  by  the  U. 
S.  government,  we  may  then  learn  something  as  to  the  direc- 
tion of  the  flow  and  its  source.  A  carefully  prepared  series 
of  analyses,  too,  may  aid  in  leading  the  way  to  the  true 
source.  There  is  infinite  room  for  investigation,  and  noth- 
ing but  room  as  yet  provided  for  the  investigator.  The 
past  season  witnessed  the  taking  of  the  first  step  leading  to 
the  determintion  of  the  source  of  these  subterranean  waters. 

Considerable  work  in  the  way  of  geological  study  and  sta- 
tistical investigation  was  done  by  the  several  members  of 
the  committee  of  Artesian  Underflow,  and  Irrigation  Inves- 
tigation, acting,  by  authority  of  Congress,  under  the  De- 
partment of  Agriculture. 

Without  entering  into  any  consideration  of  the  many 
facts  upon  which  this  committee  of  experts  based  its  opin- 
ion, as  expressed  in  its  reports  to  Congress,  I  state  briefly 
the  conclusion  reached  by  them  as  to  the  probable  source  of 
this  vast  subterranean  sea.  As  is  well  known,  the  water  is, 
in  all  cases,  found  in  the  layers  of  more  or  less  porous  and 
soft  sand-rock  which  underlies  nearly  the  whole  state  and 
extends  thence  westward,  finally  to  find  an  outcropping 
among  the  eastern  foothills  of  the  Rocky  Mountains,  and 
transverse  to  the  courses  of  most  of  the  large  rivers  which 
find  a  head  in  that  vast  drainage  area. 

Many  observed  facts  of  great  weight  would  tend  to 
prove  that  the  vast  quantities  of  water  known  to  be  lost 
to  the  Missouri,  the  Yellowstone  and  other  large  rivers, 
while  flowing  over  the  upturned  edges  of  this  outcropping 
sand-rock,  is  carried  through  these  porous  sponge-like  for- 
mations to  find  a  lodgement  beneath  the  broad  acres  of  Da- 
kota, and  an  outlet,  no  one  knows  where.  In  the  absence  of 
any  theory  having  the  support  of  better  evidence  and  a 
greater  array  of  facts  in  its  support  this  theory  as  to  the 
source  of  the  artesian  waters  will  stand.  There  seems  to  be 
little  doubt  as  to  its  correctness.  Assuming  it  to  be  correct 
that  the  fountain  head  of  our  wells  is  in  the  vast  water-shed 
of  the  Rockies  and  that  the  volume  supplied  to  this  great 
underground  river  is  what  it  is  calculated  to  be,  the  demon- 
stration is  complete  tnat  the  supply  is  absolutely  inexhaus- 
tible for  all  time  and  under  whatever  tax  it  may  serve  this 
or  future  generations. 


In  no  ease  has  a  well  failed 

or  shown  any  decrease  in  its  volume,  provided  it  has  been 
kept  clean  and  open.  Some  wells  have  become  closed  en- 
tirely but  when  cleaned  out  they  have  again  flowed  with 
their  old  time  vigor. 

What  the  thickness  or  depth  of  the  water-bearing  sand- 
rock  is,  has  not  been  determined  for  no  drill  has  yet  gone 
through  it.  Several  wells  have  been  sunk  from  50  to  75  feet 
into  this  rock  but  the  flow  has  then  become  so  powerful  as 
to  prevent  further  drilling.  It  would  be  folly  indeed  to  sup- 
pose that  the  feeble  efforts  of  man  to  gain  a  little  water  for 
his  use  would  have  any  effect  upon  the  vast  sea  of  water  be- 
neath us  the  area  of  which  is  measured  by  hundreds  of  miles 
and  the  depth  by  hundreds  of  feet.  ALL  THE  WATER  THAT 

ALL  THE  WELLS  IN  DAKOTA  CAN  THROW  FOR  A  HUNDRED 
YEARS  WOULD,  IF  GATHERED  TOGETHER,  EQUAL  A  LESSER 
VOLUME  THAN  NOW  UNDERLIES  A  SINGLE  COUNTY— BROWN. 

Figure  it  out.    This  is  no  guess. 

In  conclusion  I  quote  from  a  letter  written  by  Col.  E.  S. 
Kettleton  (The  Chief  Engineer  of  the  Department  of  Irriga- 
tion Inquiry,  of  the  U.  S.  Department  of  Agriculture.)  to 
Mr.  E.  O.  Richards  of  the  Consolidated  Land  and  Irrigation 
Co.  of  Huron,  S.  D. 

Col.  Nettletori  says: 

"  In  reply  to  your  request  for  an  expression  of  opinion  con- 
cerning the  extent  and  durability  of  the  Dakota  artesian 
water  supply  for  irrigation  purposes,  I  will  state  that  after 
two  seasons  spent  in^examining  the  artesian  wells  in  South 
Dakota,  and  their  probable  source  of  supply,  we  have  come 
to  the  conclusion  that  the  supply  comes  from  the  elevated 
and  mountainous  country  lying  to  the  west  (principally  in 
Montana),  where  the  rock  strata  are  turned  up  so  as  to  come 
to  the  surface.  The  water  is  transmitted  through  and  is  re- 
tained in  the  sand  rock,  which  is  estimated  to  be  several 
hundred  feet  in  thickness,  and  is  made  up  of  layers  (more  or 
less  fractured)  from  one  to  fifteen  feet  in  thickness,  and  of 
variable  degrees  of  hardness  and  porosity.  Below  the  strata 
are  thin  layers  of  impervious  clay,  shale,  soft  sand  and  lig- 
nite. This  formation  is  exposed  and  is  capable  of  imbibing 
a  large  amount  of  water  from  the  unfailing  supply  from  the 
mountains  and  the  mountain  streams  and  rivers,  which  have 
cut  their  way  deeply  into  the  artesian  water  bearing  rock. 
I  therefore  conclude  the  supply  will  never  fail.  It  is  natural 
to  suppose  that  the  artesian  supply  can  be  found  along  the 
entire  line  between  the  source  of  supply  and  the  present  ba- 
sin, which  has  an  extent,  north  and  south,  of  about  425 
miles.  I  am  of  the  opinion  that  the  deeper  the  water  bear- 
ing strata  are  penetrated  the  greater  will  be  the  volume  ob- 
tained." E.  S.  NETTLETON. 


Artesian.  Water  anxl  Vegetation- 

Before  irrigation  was  thought  of  in  Dakota,  and  the  water 
used  upon  grains,  the  opinion  was  frequently  expressed  that 
artesian  water  would  injure  house  plants  and  trees  and 
would  kill  grass.  Experience  has  disproved  all  of  these 
statements  for  the  most  delicate  house-plants  now  thrive  on 
this  water,  the  finest  lawns  in  our  towns  are  sprinkled  with 
it.  Of  field  grains  and  garden  truck  the  same  is  true.  Where, 
without  its  use  the  plant  would  die,  with  its  use— and  abund- 
ant use — there  is  such  an  abundant  growth  as  to  astonish  the 
grower.  Plant  growth  is  a  chemical  process  and  the  plant 
itself  a  chemical  creation  brought  about  in  the  laboratory  of 
the  earth  and  through  the  agency  of  the  air  and  water;  the 
latter  being  nature's  great  solvent  and  reagent.  From  the 
air  the  plant  derives  its  supply  of  nitrogen  and  oxygen,  and 
from  the  water  its  supply  of  hydrogen,  and,  through  the  sol- 
vent action  of  water,  its  supply  of  lime,  soda,  potash,  mag- 
nesia, iron,  manganese,  silica,  chlorine  and  other  chemicals 
all  of  which  are  indispensable  to  plant  life.  Different  plants 
require  different  chemical  ingredients  in  their  food  arid  ab- 
sorb, of  the  same  ingredient,  different  proport  ons. 

Many  analyses  have  been  made  of  artesian  waters  and  in 
no  case  has  any  showing  been  made  of  any  chemical  constit- 
uent of  the  waters  that  would  be  in  any  way  injurious  to 
plant  life  but,  on  the  contrary,  the  result  has  shown  that  the 
artesian  water  was  especially  well  adapted  to  the  fertiliza- 
tion of  our  soil  and  the  production  of  such  plants  and  grains 
as  are  best  suited  to  pur  soil  and  climate. 

The  analyses  of  this  water  show 

Silica  1    Alumina 


Sulphate  of  sodium 

"  potassium 
"         "  calcium 


Carbonate  of  lime 
iron 
Chloride  of  sodium 


"  magnesia  Traces  of  organic  matter 

"  lime.  "  phosphates, 

which  elements  are  in  varying  quantities  according  to  the 
location  of  the  well. 

The  waters  of  the  northern  wells  are  very  soft  and  this  is 
true  of  some  of  the  southern  wells,  but,  as  a  rule,  the  south- 
ern well  waters  are  harder  and  not  so  well  adapted,  on  that 
account,  to  household  uses.  The  taste  varies  greatly  but  in 
all  cases  the  water  is  palatable  when  cold  and  it  is  used  by 
thousands  of  families  for  drinking  in  preference  to  any  other 
waters.  When  warm— as  when  it  flows  from  the  well— it,  in 
some  cases,  has  a  brackish,  saline,  unpleasant  taste;  but  on 
cooling  this  disappears.  The  temperature  ranges  from  55° 
to  68°.  In  the  winter  it  will  run  in  ditches  for  several  miles 
before  freezing  and  ponds  of  it  will  remain  open  when  the 
temperature  ranges  from  10  to  40°  below  zero  for  a  week  or 
two.  This  warmth  imparted  to  the  soil  in  the  spring  forms 
a  valuable  supplement  to  the  warmth  of  the  sun,  quickens 
the  act  of  germination  and  aids  much  in  the  early  stages  of 
growth. 


77 
THE  POWER  OF  WELLS. 

It  is  not  alone  for  irrigation  and  domestic  use  that  the  ar- 
tesian waters  will  be  used  but  also  for  POWER.  The  first 
well  at  Aberdeen,  in  1882,  demonstrated  the  possibility  of 
utilizing  the  pressure  of  the  well  for  the  purpose  of  forcing 
the  water  through  water  mains,  thus  furnishing  a  system  of 
water  supply  and  fire  protection  second  to  none  in  point  of 
efficiency  and  equalled  by  none  in  economy  of  management 
and  maintenance.  No  steam  tire  engine  is  necessary  to  force 
a  stream  through  the  mains  and  hose  and  over  the  highest 
buildings;  nor  is  it  necessary  to  provide  for  the  care  and 
maintenance  of  such  an  expensive  plant  as  is  necessary 
with  a  steam  power  plant.  The  first  cost  of  the  well  was 
less  than  the  cost  of  an  engine,  and  it  fills  the  double  pur- 
pose of  supplying  the  water  and  forcing  it  wherever  it  may 
be  needed;  and  all  this  at  no  expense  other  than  an  occasion- 
al repair  to  pipe  or  valve. 

Few  there  are,  no  doubt,  in  the  many  towns  of  Dakota, 
where  there  are  systems  of  artesian  water  works,  who  ever 
pause  to  consider  what  these  towns  would  have  been  had  it 
not  been  for  these  wells;  or  what  they  would  have  done  for 
public  fire  protection  or  for  domestic  consumption,  but  for 
these  wonderful  "spouters." 

There  is  no  other  source  adequate,  other  than  to  the  Mis- 
souri river  towns,  except  to  an  occassional  town,  where 
large  surface  wells,  in  sand  formations,  might  have  supplied 
a  very  limited  public  service.  The  wells  have  been  a  God- 
send indeed.  The  application  of  the  well's  pressure  to  fire- 
pressure  service,  led  naturally  to  the  idea  of  using  it  for 
power  to  run  water  motors. 

The  first  application  of  well  power  to  the  operation  of 
machinery  was  by  the  Aberdeen  Electric  Light  Co.  They 
tapped  the  main  pipe  of  the  city's  well  with  a  %  inch  pipe 
and  with  this  stream  they  ran  the  entire  plant  for  some 
time.  This  power  wTas,  in  the  end,  abandoned  because  the 
sand  in  the  water  cut  out  the  buckets  of  the  motor. 

At  this  time  there  was  a  move  made  to  build  a  flour  mill 
to  be  operated  by  artesian  power,  but  the  project  was  aban- 
doned upon  the  advice  of  several  eastern  hydraulic  engineers 
to  whom  the  matter  was  submitted  by  the  author.  Each 
declared  it  to  be  impracticable— impossible— to  utilize  the 
power  of  these  wells,  and  such  expressions  of  opinion  are, 
even  now,  common  among  that  class  of  experts;  and  little 
credence  is  given  to  what  has  since  become  a  demonstrated 
fact. 

Soon  the  use  of  small  motors  became  quite  common,  and 
to-day  scores  of  motors  of  different  makers  are  used  to  run 
coffee  mills,  feed  mills,  printing  presses,  elevators  and  simi- 
lar classes  of  machinery.  The  first  application  of  well  pow- 
er to  the  running  of  a  flour  mill  was  at  Hitchcock,  Beadle 
county,  S.  D.,  where,  with  a  small  well  3%  inches  at  the  bot- 


78 

torn,  they  run  a  mill  grinding  from  40  to  50  barrels  of  flour 
per  day.  The  motor  is  a  simple,  home-made  wheel  and  the 
efficiency  fully  up  to  what  could  be  desired  from  an  expens- 
ive steam  plant.  The  saving  in  this  instance  is  not  alone 
the  cost  of  fuel,  oil,  engineer's  salary,  expensive  repairs  to 
boiler  and  engine,  etc.,  etc.,  but  also  the  decreased' danger 
from  fire  and  explosion  and  the  consequent  reduction  in  fire 
insurance  rates.  The  saving  in  insurance  alone  will  fully 
cover  all  the  expense  of  operation  by  the  well. power. 

This  small  well  also  supplies  the  domestic  use  and  fire 
service  of  the  town,  and  the  exhaust  water  from  the  mill 
serves  to  irrigate  a  large  farm. 

Where  on  earth,  outside  of  this  artesian  valley,  can  an- 
other showing  be  made  that  will  compare  with  this'?  (See 
page  81.) 

A  larger  mill  at  Woonsocket,  using  a  Pelton  wheel,  runs 
at  a  capacity  of  100  barrels  per  day.  (See  page  81.)  Other 
mills  at  Springfield,  Yank  ton  and  other  points  also  use  wells 
for  their  motive  power.  All  the  machinery  in  the  "Huron- 
ite"  publishing  house,  at  Huron,  S.  D.,  is  run  by  a  Chicago 
Water  Motor  connected  to  the  city  water  mains;  and  the 
electric  light  plant,  operating  both  arc  and  incandescent 
lamps,  is  run  by  a  3  foot  Pelton  wheel  connected  directly  to 
a  5%  inch  well,  which  also  supplies  water  to  the  water 
works. 

A  plant,  unique  in  this  field  and  having,  to  the  engineer,  a 
greater  degree  of  interest  than  any  other,  because  of  the 
manner  of  applying  the  water  and  the  results  accomplished, 
is,  the  sewer  plant  at  Aberdeen.  This  was  the  first  applica- 
tion of  a  well  to  the  performance  of  heavy  duty  and  it  is  the 
only  plant  of  its  kind  on  the  globe.  The  well  is  4^  inches 
at  the  bottom  and  6  inches  at  the  top,  and  has  a  volume  of 
about  1500  gallons  per  minute,  under  a  pressure  of  from  140 
to  160  pounds  to  the  inch. 

The  water  is  supplied  through  3-inch  pipes  to  two  Worth- 
ington  water  motors  and  pumps.  The  application  of  the 
water  to  the  pistons  in  the  cylinders  being  the  same  as  with 
steam  in  the  cylinders  of  a  steam  engine — the  water  operat- 
ing the  same  as  the  steam. 

When  the  two  pumps  are  running  at  the  rate  of  60  strokes  each  per  min- 
ute there  is  a  reserve  of  pressure  at  the  well  of  40  pounds  per  inch.  The 
pumps  running  at  this  rate  have  a  capacity  of  2,500.000  gallons  per  day  of 
sewage  pumped  a  vertical  distance  of  23  feet.  When  on  their  tour  of  in- 
spection the  U.  S.  Senate  committee  on  irrigation  investigation  pronounc- 
ed this  plant  to  be  the  most  wonderful  adaptation  of  the  power?  of  nature 
that  had  come  under  their  observation. 

Any  man  who  believes  that  a  well  cannot  be  successfully  harnessed  to  a 
load  needs  but  to  witness  the  operation  of  this  plant  to  be  convinced  that 
he  is  in  error,  for  when  a  well,  through  the  agency  of  proper  machinery, 
will  lift  a  load  of  twenty  millions  of  pounds  a  day  through  23  feet,  or  479 
millions  of  pounds  one  foot  high  in  a  day,  that  well  may  be  fairly  said  to 
have  performed  a  good  day's  WORK. 

Experts  to  the  contrary,  the  artesian  wells  of  Dakota  supply  the  most 
wonderful  power  on  the  globe.  The  stupenduous  unutilized,  and  to  a 
great  extent,  unavailable  power  of  mighty  Niagara  must  pale  in  compari- 
son with  the  power  of  Dakota's  artesian  wells. 


79 

Here  no  special  mill  site  must  be  chosen  and  then  pur- 
chased of  the  owner  at  his  own  figures,  for  every  inch  of  our 
broad  domain  is  as  good  a  mill  site  as  there  is  on  the  earth. 
The  ground  here  has  but  to  be  opened  in  order  to  pour  forth 
the  flood  which  will  serve  not  one  purpose  alone  but  many. 

Power,  domestic  use,  fire  protection,  irrigation,  and  even 
heat  are  but  the  chief  among  the  many  duties  to  which  a 
well  may  be  called.  More  there  are  which  will  soon  find  a 
place  in  the  every  day  economy  of  Dakota  life;  and  all  com- 
bined will  soon  be  the  chief  factors  in  making  this  the  won- 
derland of  America. 

Every  well  owner  who  can  afford  it  should  have  a  motor, 
for  with  it  much  labor  of  the  farm  may  be  performed.  A 
very  small  expense,  added  to  a  little  ingenuity  and  home  la- 
bor, will  harness  the  churn,  the  feed  mill,  the  fanning-mill, 
the  feed-cutter,  the  threshing  machine,  the  grindstone  and 
other  farm  machines  to  the  motor  and  thus  save  a  vast 
amount  of  labor,  expense  and  even  life  itself.  Any  farmer 
will  appreciate  the  great  advantage  of  having  his  threshing 
done  by  water  power  instead  of  by  steam  power,  in  which 
latter  case  there  is  the  constant  danger  from  fire  and  explo- 
sion. 

All  these  things  will  come,  in  time,  for  Dakota's  farmers 
are  too  enterprising  to  long  delay  the  utilization  of  the 
forces  thus  gratuitously  laid  at  their  feet.  Lack  of  means 
is  the  only  obstacle  to  the  proper  utilization  of  that  which, 
ere  long,  will  transform  Dakota  into  the  most  productive, 
prosperous,  wealthy,  and  wonderful  agricultural  region  in 
this  or  any  other  land. 

Nor  will  capital  long  hold  back  when  it  has  been  fully 
assured  01  the  successes  already  achieved  by  the  pioneers  in 
the  field  of  irrigation  and  the  development  of  artesian  pow- 
er. No  more  profitable  investment  can  be  found  to-day  than 
such  as  is  made  in  Dakota  lands  on  which  wells  are  placed, 
or  in  the  development  of  this  inexhaustable  power  that 
flows  not  to  wreck  and  to  ruin  but  to  fructify  and  enrich. 
It  becomes,  then,  the  duty  of  every  lover  of  Dakota  to  her- 
ald the  great  truths  (unembellished  by  any  exaggerations)  as 
to  the  wonderful  possibilities  that  we  ourselves  have  but 
just  begun  to  appreciate. 

The  ear  of  capital  will  be  reached  if  we  but  call  long  and 
loudly,  and  when  reached  the  means  will  cease  to  be  the  ob- 
stacle to  success  which  now  awaits  us. 

On  page  81  will  be  seen  the  reports  of  some  of  the  millers 
of  the  state  as  to  the  service  rendered  them  by  artesian 
wells.  In  the  face  of  such  facts  no  argument  need  be  given 
to  prove  the  great  value  to  Dakota  of  this  great  source  of 
power.  The  reports  are  from  points  widely  separated  which 
shows  the  extent  of  the  field. 


80 


TABLE  FOR  CALCULATING  THE    HORSE    POWER 
OF  WATER. 

The  following  table  gives  the  horse  power  of  one  cubic 
foot  of  water  per  minute  under  different  heads. 

TABLE  NO.  32. 

Adapted  from  Peltou  \Vat»»r  \VlxM-l  ( '<>, 


Heads  in 
feet. 

Pressure  per    Horse 
Sq.  inch,  Ibs.   Power. 

Heads  in 
feet. 

Pressure  pi«r 
sq.  inch,  Ibs. 

Horse 

Power. 

1 

.43 

.001609S 

310 

134- 

.49903S 

20 

8.66 

.032196 

320 

138 

.515138 

30 

.  12.99 

.048294 

330 

143 

.531234 

40 

17.32 

.064392 

340 

147 

.547332 

50 

21.65 

.080490 

350 

152 

.563430 

60 

25.99 

.096588 

380 

156 

.579528 

70 

30.32 

.112686 

370 

160 

.595626 

80 

34.65 

.128784 

380 

164 

.611724 

90 

38.98 

.144X92 

390 

169 

.627X22 

100 

43.31 

.  160980 

400 

173 

•  .643920 

110 

47.64 

.  177078 

410 

178 

.660018 

120 

51.98 

.  193176 

420 

\^2 

.676116 

130 

56.31 

.209274 

430 

186 

.692214 

140 

60.64 

.225372 

440 

191 

.708312 

150 

64.97 

.241470 

450 

195 

.724410 

160 

69  31 

.257568 

460 

199 

.740508 

170 

73.64 

.273666 

470 

204 

.756606 

180 

77.97 

.  289764 

180 

206 

.772704 

190 

82.30 

.305862 

490 

212 

.788802 

200 

86.63  j    .321960 

500 

216 

.804900 

210 

90.96      .33,SO:>(s 

520 

22r> 

.837096 

220 

95.30      .354156 

540 

231 

869292 

230 

99.63  ;     .370254 

560 

243 

.901488 

240 

103.90      .3*6352 

580 

251 

.9:53684 

250 

108.29  j     .402450 

600 

200 

.965880 

260 

112.62  !    .418548 

650 

282 

1.046370 

270 

116.96      .434646 

700 

303 

1  .  126S60 

280 

121.29      .450744 

750 

325 

1.207350 

290 

125.62 

.466842 

800 

346 

1.287840 

300 

129.95 

.482940 

900 

390 

1.448820 

When  the  Exact  Head  is  found  in  the  Table. 

EXAMPLE— Have  100  foot  head  and  300  cubic  feet  of  wa- 
ter. How  many  horse  power  have  I  ? 

From  table— H.  P.  for  100  ft.  head =.160980  for  1  cu.  ft.  of 
water,  hence  .160980x300=48.294  the  H.  P.  for  300  cu.  ft.  per 
minute. 

From  table  3(5  we  find  that  300  cu.  ft.=2244  gallons. 

If  a  well  having  a  flow  of  2244  gallons  per  minute  will,  while 
throwing  that  amount,  show  a  pressure  of  43  Ibs.  per  inch 
(=100  ft.  head)  then  it  will  develop  48.29  effective  horse  power. 

When  Exact  Head  is  not  found  in  the  Table 

Take  the  H.  P.  of  1  cu.  ft.  under  1  foot  head  and  multiply 
by  the  number  of  ft.  head  given,  then  by  the  number  of  cu. 
ft  given.  The  product  will  be  the  required  H.  P. 

NOTE — The  table  is  based  upon  an  efficiency  of  85  percent. 

Note  the  fact  that  a  well  shows  no  pressure,  or  head,  when  discharging 
its  full  volume.    Turn  it  off  a  little  so  as  to  get  some  pressure,  then  meas- 
ure volume  and  proceed  according  to  above  table  to  calculate  the  power. 
See  page  82. 


81 
WOOXSOCKET  MILL. 

Northy  and  Duncan  of  the  Woonsocket  mill  report  as  fol- 
lows: Our  well  is  775  feet  deep;  7  inches  in  diameter  all  the 
way;  pressure  135  Ibs.  when  closed;  62  Ibs.  with  a  4-inch 
opening,  75  Ibs.  with  a  3-inch  opening.  We  use  a  3  foot 
PEL-TON  wheel,  Tunning  at  275  revolutions  per  minute,  the 
nozzle  throwing  a  1%  inch  stream.  Wahave  made  88  bar- 
rels of  flour  and  36  tons  of  good  feed  per  day  of  24  hours, 
and  we  figure  on  a  saving  of  from  $14  to  $17  per  day  as  com- 
pared with  steam  power  of  equal  service.  The  element  of 
safety  being  worth  much  that  cannot  be  expressed  in  figures. 

SPRINGFIELD  MILL. 

Mr.  J.  J.  Kattleman  of  the  Springfield  mill  reports  as  fol- 
lows: Our  well  is  593  feet  deep,  and  8  inches  all  the  way. 
The  pressure,  when  closed,  is  80  Ibs.,  and  when  mill  is  run- 
ning it  is  40  Ibs.  We  use  a  16-inch  turbine  wheel,  making 
about  800  revolutions  per  minute.  The  well  cost  $3,000,  but 
could  be  drilled  for  less  now.  We  put  out  about  60  barrels 
of  flour  per  day,  and  figure  on  a  saving  of  from  $12  to  $15 
per  day  as  against  steam  power.  This  item  alone  being  a 
handsome  profit  or  interest  on  the  cost  of  the  well.  Repairs 
are  very  light  and  insurance  much  less  than  with  steam. 
We  get  over  42  horse  power  from  the  well. 

YANKTOX-"FOUNTAIN"  AND  "EXCELSIOR"  MILLS. 

Mr.  E.  Miner  of  the  Fountain  Roller  Mills  of  Yankton  says :  Well  is  600 
feet  deep,  6  inches  in  diameter,  pressure  from  48  to  56  pounds  per  inch,  and 
flows  from  1600  to  2000  gallons  per  minute.  We  use  a  Dubuque  turbine  wheel 
12  inches  in  diameter  and  of  guaranteed  27  horse  power.  The  cost  of  the 
power  plant,  complete  to  run,  was  about  $4,000.  We  pay  3  per  cent  insur- 
ance and  would  pay  4V£  or  5  if  running  by  steam.  I  think  we  are 
paving  over  $8  per  day  as  compared  with  an  engine.  Our  mill  is  one  of  40 
barrel  capacity. 

F.  L.  Van  Tassell  of  the  Excelsior  Mill  Co.,  says :  Our  well  is  500  ft.  deep, 
pipe  8  inches  to  the  bottom;  pressure  when  closed  52  Ibs.,  with  1  inch 
opening  48  Ibs.,  with  2  inch  opening  42  Ibs.,  with  4  inch  opening  20  Ibs.  ; 
water  clear  and  hard.  We  use  a  PELTON  wheel  6  feet  diameter  with  23£ 
inch  nozzle,  revolutions,  125  per  minute.  Power  about  30  horse.  We  run 
our  elevator  and  raise  about  500  bushels  of  wheat  per  hour,  shell  100  bush- 
els of  corn  and  grind  4000  Ibs.  of  feed  per  hour.  Will  soon  attach  all  the 
mill  machinery  to  the  well.  The  well  flows  3000  gallons  per  minute,  and, 
with  wheel,  power  house,  etc..  cost  about  $4,000.  Cost  of  running  it  prac- 
tically nothing,  so  saving  per  year  as  compared  with  steam  power  is  very 
great. 

HITCHCOCK  MILL. 

Mr.  M.  B.  Potter  of  the  Hitchcock  Milling  Co.,  says :  Size  of  well  4  inches 
at  top.  3  inches  at  the  bottom.  Depth  960  feet.  Volume  1240  gallons  per 
minute.  Pressure  when  closed  155  pounds.  With  1  inch  opening  140 
pounds.  With  2  inch  opening  82  pounds.  WTe  get  about  30  horse  power 
from  a  wheel  of  our  own  design,  it  being  50  inches  in  diameter  and  runs 
at  about  300  revolutions  per  minute.  The  well  cost  the  town  $4,500.  We 
have  had  no  expense  for  repairs  since  putting  in  the  wheel  in  June,  1890 
—nearly  3  years.  The  mill  has  a  capacity  of  50  barrels  in  24  hours.  Be- 
sides running  the  -mill  the  well  supplies  water  to  the  town,  maintains 
water  in  an  artificial  lake,  and  waters  an  irrigated  farm.  The  well  has 
been  running  since  1886  and  the  volume  is  invariable  and  apparently  inex- 
haustible and  the  pressure  is  uniform. 


82 
HOE8E  POWER. 

A  horse  power  issuch  a  power  as  will  raise  83,000  pounds 
one  foot  high  in  one  minute  of  time.  The  term  is  one  of 
mechanics  and  does  not  fairly  represent  the  power  of  the 
average  horse  which  is  only  about  two-thirds  as  much. 

To  calculate  the  horse  power  of  falling  water  multiply  to- 
gether the  number  of  cubic  feet  of  water  falling  per  minute, 
the  vertical  distance  (head)  through  which  it  falls,  and  the 
number  62.3  (approximate  weight  of  1  cubic  foot  of  water) 
and  divide  the  product  by  33000. 

EXAMPLE  —  A  well  discharges  800  cubic  feet  per  minute 
from  a  pipe  16  feet  above  the  surface,  what  is  the  horse 
power  of  the  well  V 

80Qcu.ft.Xl6ft.X62.31bs,      797440 
*e,  _  -24.17  H.  P. 


This  is  the  theoretical  H.  P.  The  actual  H.  P.  as  realized 
from  machinery  will  be  less  because  the  wheel  or  motor 
does  not  realize  the  full  efficiency  of  the  water.  The  per- 
centage of  efficiency  realized  will  depend  on  the  form  of  the 
wheel  and  the  skill  of  the  makers.  It  will  range  from  25  to 
90  per  cent,  of  the  full  power.  Turbine  wheels  realize  from 
75  to  85  per  cent,  of  the  power  and  impact  wheels  about  the 
same  amount. 

The  table  on  the  next  page  will  prove  of  value  in  this  con- 
nection. 

TO  GET  THE  VELOCITY  OF  THE  FLOW  OF  A  WELL. 

If  the  volume  has  been  accurately  measured. 

Divide  the  volume  of  the  flow,  in  gallons,  by  the  volume  in 
gallons  contained  in  one  foot  of  the  pipe  of  the  well  (—the 
area  of  the  cross  section  of  the  pipe).  The  answer  will  be 
the  velocity  in  feet  per  minute. 

Thus—  Suppose  a  6-inch  well  throws  1836  gallons  per  min- 
ute, what  is  its  velocity  of  discharge  in  feet  per  minute  ? 

From  table  No.  26  we  see  that  1  foot  of  6-inch  pipe  con- 
tains 1.469  gallons.  How  many  feet,  therefore,  will  it  take 
to  hold  1836  gallons  ?  1836-^1.  469  =1250=  the  number  of  feet 
necessary  to  hold  1836  gallons,  or  the  length  of  the  column 
of  water  thrown  out  each  minute,  or  the  velocity  in  feet  per 
minute.  1250-^-60=20.8,  the  velocity  in  feet  per  second. 

This  is  the  same  as  the  rule  for  finding  the  velocity  of  any 
stream,  viz:  Divide  volume  per  minute  by  area  of  section  to 
get  velocity  per  minute,  and  divide  this  quotient  by  60  to  get 
velocity  per  second. 
To  Compute  the  Volume  of  Discharge  per  Minute. 

RULE—  Multiply  the  area  of  the  wet  section  in  sq.  ft.  by 
the  velocity  in  feet  per  second  to  get  volume  in  cubic  ft,  per 
sec.  Multiply  this  product  by  60  to  get  the  volume  per  min. 
To  Compute  the  Height  of  the  Head  in  Feet. 

RULE—  Divide  the  volume  in  cu.  ft.  per  second  by  the 
area,  and  the  square  of  this  quotient,  divided  by  64.33,  will 
give  the  height  of  the  head  in  feet. 


83 

TABLE  NO.  33. 

TABLE  SHOWING  FLOW  PER  MINUTE  EQUAL  TO 
A  GIVEN  FLOW  PER  DAY  AND  TOTAL  FLOW 
PER  DAY  FROM  A  GIVEN  FLOW  PER  MINUTE. 

New. 

Total  gallons  perj    Equal  gallons   ij      Gallons  per       Equal    gallons  per 


(lay. 

per  minute. 

minute. 

day. 

100 

.07 

.1                         144 

200 

.14 

.2 

288 

300 

.21 

.3 

432 

400 

.28 

.4 

576 

500 

.96 

.5 

720 

600 

.42 

.6 

864 

700 

.49 

.7 

1008 

800 

.56 

.8 

1152 

900 

.63 

•  9 

1296 

1000 

.7 

1. 

1440 

2000 

1.4 

2. 

2880 

3000 

2.1 

3. 

4320 

4000 

2.8 

4. 

5760 



5000 

3.5 

5. 

7200 

6000 

4.2 

6. 

8640 

. 

7000 

4.9 

7. 

10080 

I      ''     ; 

8000 

5.6 

8. 

11520 

\ 

9000 

6.3 

9. 

12960 

\    O 

10000 
25000 

6.9 
17.4 

10 
25 

14400 
36000 

^t 

50000 

34.8 

50 

72000 

^.N 

75000 

52.2 

75 

108000 

100000 

69.5 

100 

144000 

200000 

138.9 

200 

288000 

300000 

208.3 

300 

432000 

400000 

277.8 

400 

576000 

500000 

347.2 

500 

720000 

600000 

416.7 

600 

864000 

700000 

486.1 

700 

1008000 

800000 

555.6 

800 

1152000 

900000 

625.0 

900 

1296000 

1000000 

694.5 

1000 

1440000 

2000000 

1388.9 

2000 

2880000 

3000000 

2083.3 

3000 

4320000 

4000000 

2777.8 

4000 

5760000 

5000000 

4372.2 

5000 

7200000 

6000000 

4166.7 

6000 

8640000 

7000000 

4861.1 

7000 

10080000 

8000000 

5555.6 

8000 

11520000 

9000000 

6250.0 

9000 

12960000 

10000000 

6944.5 

10000 

14400000 

This  table  will  be  most  convenient  in  making  quick  com- 
parisons as  between  different  wells  in  Dakota  and  those 
elsewhere  where,  as  a  rule,  the  flow  is  reported  as  so  much 
per  day  while  in.Dakota  the  flow  is  always  so  much  per  min- 
ute. The  greatest  wells  outside  of  Dakota  are  those  of  Kern 
Co.,  California,  which  flow  from  150,000  to  4,000,000  gallons 
per  day  or  (see  table)  from  104.3  (69.5  +  34.8)  to  2,777.8  gallons 
per  minute.  Of  their  54  wells  only  10  flow  over  1,200,000  gal- 
lons per  day  or  833  4  gallons  per  minute.  This  table  shows 
at  a  glance  the  superiority  of  the  Dakota  wells. 

Example  of  use  of  table.  How  many  gallons  per  minute 
flow  from  a  well  throwing  5,359,800  gals,  per  day  ?— Add  the 
quantities  in  2d.  column  3,472.2  +  208.3  +  34.8  +  6.3+  .56 
—  3,722.16  gallons  per  minute. 


84 


85 

By  interpolation  other  quantities  may  be  readily  taken 
from  the  foregoing  table ;  thus— 

To  cover  10  acres  8%  inches  deep, 

Multiply    36,300  (amount  for  1  inch)  by  8  =    290,400 

and  add  J£  of  36,300    "        "    "    '"  =      18,150 

Total  =    308,550  cu.  ft. 

Where  the  required  acres  and  the  required  depth  are 
neither  one  in  the  table  as— Required  the  cu.  ft.  to  cover  17 
acres  7  inches, — proceed  thus — 

Take  out  quantity  for  1  acre  and  multiply  by  the  given 
number  of  acres. 

Thus  —  To  cover  1  acre  6  inches  21,780 

"       1    "     1  inch  3,63G 

"      1    «'     7  inches  ,25,410 

25,410  x  17,  the  given  number  of  acres  =  431,970  cubic  feet, 

OB  if  the  inches  cannot  be  taken  from  the  table  as  in  above 

case  multiply  the  amount  for  one  inch  by  the  given  number 

of  inches,    Thus,  amount  for  11  inches  =   3630  (amount  for 

one  inch)  x  11  =  39,930  cu.  ft. 

The  volume  in  gallons  may  be  found  by  multiplying  the 
total  cu.  ft.  by  7.48052,  the  number  of  gallons  in  one  cu.  ft. 

or 

by  interpolation  from  Section  B.  How  many  gallons  in 
308,550  cu.  ft.  (amount  to  cover  10  acres  8J^  inches  deep)  ? 
From  Section  B.  we  find  3,258,500  as  gals,  to  cover  10  acres  1 
foot  or  24  half  inches;  8)£  inches  =  17  half  inches,  therefore, 
divide  3,258,500  by  24,  to  get  amount  for  one  half  inch,  and 
multiply  this  quotient  by  17  to  get  gals,  for  17  half  inches. 

OR  see  table  No.  36 

The  time  required  for  a  well  of  given  volume  per  minute 
to  throw  any  given  quantity  of  water  is  found  by  dividing 
the  total  volume  by  the  volume  of  the  well  per  minute  and 
then  reduce  the  number  of  minutes  thus  found  to  hours, 
days,  weeks,  &c.  or 

If  the  quantity  is  given  in  the  foregoing  table  take  out  the 
time  from  Section  C.  or,  if  the  quantity  is  not  given  in  the 
table  proceed  as  in  the  following.  Example:  9  inches  deep 
on  100  acres  from  a  500  gal.  well  will  take— 


2,178,000  cu.  ft.  =  6  inches. ) 
1,089.000   "    "    =  3     " 
3,267,000  cu.  ft.  =  9  inches.  J 


»._»_  32,585,000  =  gals,  on  100  Ac.  1  ft.  deep 
A  n  (Sec.  B.)  divided  by  12  =  2.715,417  X  9 
A  =  24,438,753  =  gals,  at  9  inches. 

From  Section  C  we  find  it  takes  a  500  gal.  well  1  mo.,  15  ds.,  6  hrs.,  to 
cover  100  acres  12  inches  deep,  or  1,086  hours.  Since  9  =  3£  of  12  take  2£  of 
1,086  hours  =  813  hours  or  33  days  and  21  hours.  Ans. 

From  table  35  (next  page)  an  approximation  may  be  quickly  taken. 
Thus,  under  head  of  500  gal.  well  we  see  21.600,000  =  gals,  thrown  in  1  mo. 
and  720,000  =  gals,  in  1  day.  720.000  X  4  =  2,880,000  gals,  which  added  to 
21,600,000  gals.  =  24,480,000  gals,  in  34  days,  or  a  little  more  than  our  esti- 
mated amount  of  24,438,753  gals.  From  this  it  is  shown  that  the  amount 
will  be  thrown  in  a  little  less  than  34  days  (33  ds.  21  hours  as  above.) 

For  exact  amounts  and  times  one  should  figure  exactly  which  may  be 
done  from  the  tables  by  using  a  few  more  figures. 


86 


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87 


TABLE  NO.  36. 

TABLE  SHOWING  EQUIVALENCE  OF  CUBIC  FEET 
AND  GALLONS— AND  GALLONS  AND 

CUBIC    FEET.  New. 


Cubic  feet  to  gallons. 

Gallons  to  cubic  feet. 

Cubic  feet.      = 

=        Gallons. 

Gallons.         = 

Cubic  feet. 

1 

2 

7.48 
14.96 

1 
2 

.133679 
.267:358 

3 

22.44 

3 

.401037 

4 

29.92 

4 

.534716 

5 

37.40 

5 

.668395 

6 

44.88 

6 

.802074 

7 

52.36 

7 

.935753 

8 

59.84 

8 

1.069432 

9 

67.32 

9 

1.203111 

10 

74.80 

10 

1.336790 

20 

149.61 

20 

2.673580 

30 

224.41 

30 

4.010370 

40 

299.22 

40 

5.347160 

50 

374.02 

50 

6.683950 

60 

448.83 

60 

8.020740 

70 

523.63 

70 

9.357530 

80 

598.44 

80 

10.694320 

90 

673.24 

90 

12.031110 

100 

748.05 

100 

*      13.367 

200 

*     1496 

200 

26.735 

300 

2244 

300 

40.103 

400 

2992 

400 

53.471 

500 

3740 

500 

66.839 

600 

4488 

600 

80.207 

700 

5236 

700 

93.575 

800 

5984 

800 

106.943 

900 

6732 

900 

120.311 

1000 

7480 

1000 

*         133 

2000 

14961 

2000 

267 

3000 

22441 

3000 

401 

4000 

29922 

4000 

534 

5000 

37402 

5000 

668 

6000 

44*883 

6000 

802 

7000 

52*363 

7000 

935 

8000 

591844 

8000 

1069 

9000 

67J324 

9000 

1203 

10000 

74*805 

10000 

1336 

100000 

748^052 

100000 

13367 

1000000 

7480520 

1000000 

133679 

10000000 

74805200 

10000000 

1336790 

100000000 

748  052  000 

100000000 

13367900 

Note  change  in  location  of  decimal  point  at  *  : 
This  table  will  be  of  great  use  in  quickly  converting  cubic  feet  to  gal- 
lons or  vice  versa. 

Example,  How  many  gallons  in  a  reservoir  containing  6,450,620  cu.  ft.? 
Take  from  the  table  the  gallons  for  1,000,000  cu.  ft.  and  X   it  by  6,   also 
the  gallons  for  100,000  cu.  ft.  and  X  it  by  4,  &c.,  as  shown  below. 

OR 

Multiply  the  total 
cubic  feet  b  y 
7.48052 ,  the  gallons 
in  one  cubic  foot 
This  requires, 
more  figures. 


7,480,520  X  6  =  44,883,120.       =  gals  for  6  000  000  cu  ft 
748,052X4=    2,992,208.       =     "  400000" 


74,805  X  5  = 
600  = 


374,025. 

4,488.        = 
149.61.  = 


50000 
600 
20 


Total  yards  =  48,253,990.61 .  = 


6  450  620 


S8 
TABLE  NO.  37. 

Table  showing  volume  in  gallons  and  in  cubic  feet  thrown  by  wells 
of  different  volumes  per  minute,  in  periods  of  one  month  (30  days) 
and  three  months  (90  days).  New. 


ONE    MONTH. 

THREE    MONTHS. 

Gallons    per 
MINUTE 

thrown  by 
well. 

rotal     gallons 
thrown  in 
1  month. 
(30  ds.) 

Equivalent 
volume    in 
ucbic  feet. 

otal     gallons 
thrown    in 
3   months. 
(90  ds.) 

Equivalent 
volume    in 
cubic  feet. 

1 

43200 

5  775 

129600 

17325 

5 

216000 

28873 

648  00  > 

86619 

10 

432000 

57748 

1  s?96  000 

173244 

20 

864000 

115  497 

2592000 

346  491 

25 

1080000 

144  373 

3  240  000 

433119 

30 

1  296000 

173  247 

3888000 

519  741 

40 

1728000 

230996 

5184000 

692988 

50 

2160000 

6480000 

866  235 

60 

2592000 

346  495 

7776000 

1  039  485 

70- 

3024000 

404244 

9072000 

1  212  732 

80 

3  456  000 

461  993 

10  868  000 

1  385  979 

90 

3888000 

519  743 

11  664  000 

1  559  229 

100 

4  320  000 

577  492 

12  960  000 

1  732  476 

200 

8640000 

1  154  986 

25  920  000 

3464958 

300 

12  960  000 

1  732  479 

38  880  000 

5  197  437 

400 

17  280  000                2  309  972 

51  840  000 

6  929  916 

500 

21  600  000                2  887  466 

64800000 

8662398 

600 

25920000          '     3464959 

77  760  000 

10  394  877 

700 

30  240  000                4  042  452 

90720000 

12  127  356 

•        800 

34560000               4619945 

103  680  000 

13859835 

900 

38880000 

5  197  439 

116  640  000 

15  592  317 

1  000 

43200000 

5  774  932 

129  600  000 

17  324  796 

1100 

47  520  000 

6  352  425 

142  560  000 

19  057  275 

1  200 

51  840  000 

6  929  919 

155  5  0  000 

20  789  757 

1  300 

56  160000 

7507411 

168480000 

22  522  233 

1400 

60  480  000               8  084  905 

181  440  000 

24  254  715 

1500 

64800000 

8  662  399 

194  400  000 

25  987  197 

1600 

69120000 

9  239  891 

207360000 

27  719  673 

1700 

73440000 

9  817  385 

220  320  000 

29  452  155 

1800 

77760000 

10  394  878 

233280000 

31  184  634 

1900 

82080000 

10  972  372 

246  240  000 

32  917  116 

2000 

86400000 

11  549  865 

259  200  000 

34  649  595 

2100 

90720000 

12  127  358 

272  160  000 

36  382  074 

2200  . 

95040000 

12  704  852 

285  120  00') 

38  114  556 

2300 

99360000 

13  282  344 

298  080  000 

39  847  032 

2400 

103680000 

13  859  838 

311  040  000 

41  579  514 

2500 

108000000 

14  437  332 

324000000 

43  311  996 

3000 

129600000 

17  324  798 

388800000 

51  974  394 

3500 

151  200000 

20  212  264 

453600000 

60  636  792 

4000 

172  800  000 

23  099  731 

518  400  000 

69  299  193 

4500 

194400000 

25987197 

583200000 

77  961  591 

5000 

216000000 

28  874  664 

648000000 

86  623  992 

5500 

237600000 

31  762  130 

712  800  000 

95  286  390 

6000 

259200000 

34  649  596 

777  600  000 

103  948  788 

7000 

302400000 

40  424  529 

907200000 

121  273  587 

8000 

345600000 

46  199  562 

1  036  800  000 

138  598  686 

9000 

388800000 

51  974  395 

1  166  400  000 

155  923  185 

10000 

432000000 

57  749  328 

1  296  000  000 

173  247  984 

See  explanation  on  opposite  page. 


89 

The  table  on  opposite  page  is  an  extension  of  table  on  page 
86,  but  changed  to  give  two  periods  or*  time  and  wells  of  a 
greater  range  of  volume  per  minute;  and  giving  the  volumes 
in  both  gallons  and  cubic  feet.  The  irrigation  season  lasts 
about  three  months  and  is  preceded  in  the  spring  and  fol- 
lowed in  the  f  11  by  about  equal  periods  of  time,  so  that  one 
month  and  three  months  are  the  periods  assumed  to  be 
those  upon  which  the  greater  number  will  desire  to  base 
estimates  as  to  the  volumes  they  can  count  on  during  these 
periods.  By  simple  addition  the  volume  of  any  well  may  be 
taken  from  the  table. 

EXAMPLE— What  volume  will  a  well  with  a  volume  of  3572  gals;  per  min- 
ute throw  in  3  months? 

3000  gal.  weU  =  388,800,000  gals.  — 51,974,1394  cu.  ft. 
500    "        "     =    64,800,000    "    -  8,662,398        " 
70    "        "     =      9,072.000    "    —  1,212,732 
2    "        "     =         259,200    "    -       34,650        " 


3572    "        "  462,931,200  61,884,174 

Having  the  amount  for  3  months,  the  amount  for  any 
lesser  or  greater  time  may  be  found  by  division  or  addition. 
Thus:  In  above  example  the  well,  in  40  days,  would  throw 
£+£=(30  ds.+lO  ds.)  of  the  total  amount  or  volume  shown; 
or  in  4J£  months  a  well  would  throw,  total  +£-f-£r=(3  Mo.+l 
Mo  -\-%  Mo)  of  the  total  volume  shown. 

The  table  will  be  found  useful  for  taking  out  rapid  approximations  as 
to  volumes  and  in  this  will  answer  the  purpose  of  the  proceeding  table — 
table  37— thus,  by  inspection  it  is  shown  that  a  reservoir  holding  about 
36,000,000  cu.  ft.  holds  about  272,000,000  gals,  and  that  a  2100  gal.  well  would 
be  required  in  order  to  fill  it  in  about  3  months. 


TABLE  NO.  38. 

DISCHARGE  OF  JETS  IN  GALLONS  PER  MINUTE. 


Head  on 
Jet 
in  Pounds. 

Head  on 
Jet 
in  feet. 

Discharge  from  Jets  of  following  diameters. 

X 

1  inch. 

IK 

1J4 

1% 

Itt 

20 

46.16 

70.4 

125.2 

158 

196 

237 

282 

25 

57.70 

78.7 

140.0 

177 

219 

265 

315 

30 

69.24 

86.3 

153.4 

194 

240 

290 

345 

40 

92.32 

99.6 

177.1 

224 

277 

335 

398 

50 

115.40 

111.4 

198.0 

251 

309 

374 

445 

60 

138.48 

121.9 

216.8 

274 

339 

410 

488 

70 

161.56 

131.8 

234.3 

297 

366 

443 

527 

80 

184.64 

140.8 

250.3 

317 

391 

473 

563 

90 

207.72 

149.4 

265.6 

336 

415 

502 

598 

100 

230.80 

157.5 

280.0 

354 

437 

529 

630 

110 

253  88 

293  6 

372 

459 

555 

661 

120 

276.96 

306.7 

388 

479 

580 

690 

130 

300  04 

319  2 

404 

499 

604 

718 

140 

323.12 

1531.2 

419 

518 

626 

745 

150 

346  20 

434 

536 

649 

772 

160 

369  28 

448 

553 

670 

797 

170 

392.36 

570 

690 

823 

180 

415.44 

710 

845 

This  table  is  calculated  from  the  formula  given  on  page  73  except  that 
H.  (head)  in  feet  is  taken  at  2.308  ft.  per  pound  of  head  instead  of  2.311  as 
given.  The  difference  is  not  material. 


90 


WIND  MILLS. 

The  following  tables  are  from  a  circular  issued  by  the  U 
S.  Department  of  Agriculture,  office  of  Irrigation  Inquiry. 

TABLE  NO.  39. 

SIZE  AND  CAPACITY  OF  WIND  MILLS  AT  VARIOUS  DEPTHS. 


Diameter 
of  wheel 
in  feet 

25  ft.  Eelevation. 

50  ft.  Elevation. 

100  ft.  Elevation. 

Size  of 
pump  in  in. 

Gallons 
per  hour. 

Size  of 
pump,  ins. 

Gallons 
per  hour- 

Size  of 
pump,ins 

Gallons 
per  hour. 

10 
12 
14 
16 

3y2 

4 
5 

6 

500 
750 
1150 
1500 

3 
8H 

300 
500 
800 
1200 

21/2 
3 
3K 

200 
350 
550 

800 

This  table  is  only  intended  as  a  general  guide  and  is  subject  to  modifi- 
cation by  reason  of  some  mills  having  greater  capacity,  for  given  size, 
than  other  mills  ;  and  the  same  applies  to  the  pump  used  and  the  manner 
of  attachment. 

TABLE  NO.  40. 

VOLUME  OF  WATER  PUMPED  PER  MINUTE. 

From  10  to  100  Feet. 


Diameter 
of 
wheel 

Vertical  distance  from  water  to  point  of  delivery,  in  feet. 

10 

15 

25 

50 

75 

100 

Feet 
8.5 
10 
12 
14 
16 
18 
20 
25 
30 

Gallons 
15.24 
48.26 
86.71 
111.67 
155.98 
249.93 
309.60 
532.52 
1080.11 

Gallons 
10.16 
32.18 

57.81 
74.44 
103.99 
159.95 
206.40 
355.01 
728.83 

Gallons 
6.16 
19.18 
33.94 
45.14 
64.60 
97.68 
124.95 
212.38 
430.85 

Gallons 
3.02 
9.56 
17.95 
22.57 
31.65 
52.17 
63.75 
106.96 
216.17 

Gallons 

Gallons 

6.64 
11.85 
15.30 
19.54 
32.51 
40.80 
71.60 
146.61 

4.25 
8.49 
11.25 
16.15 
24.42 
31.25 
49.73 
107.71 

VELOCITY  OF  WIND. 

-  The  average  over  the  U.  S.,  as  determined  by  signal  service  examina- 
tions, is  5769  miles  per  month,  or  about  8  miles  per  hour.  See  page  91— 
~table  of  wind  velocity  in  Dakota .  Experience  has  demonstrated  that  to 
operate  a  wind  mill,  there  is  required  an  average  velocity  of  wind  of  6 
miles  per  hour. 

TABLE  NO.  41. 

VELOCITY  AND  FORCE  OF  WIND.- 


Miles 
per 
hour. 

Feet 
per 
minute. 

Pressure 
per  sq.  ft. 
inlbs. 

Description 
of  the  wind. 

1  to  3 
6 

88—264 
440 

.005—  .045 
.125 

Just  perceptible 
Pleasant  wind 

10 

880 

.5 

Fresh  breeze 

20 

1760 

2. 

Stiff  breeze 

30 

2640 

4.5 

High  wind 

45 

3960 

10.125 

Gale 

60 

5280 

18. 

Great  storm 

80 

7040 

32. 

Hurricane 

100 

8800 

50.          1  Tornado 

The  mean  weight  of  the 
air  will  support  a  column 
of  water  33.95  ft.  high,  at 
sea  level.  The  velocity  of 
sound  in  air  at  60°  =  1107 
ft.  ,in  water  about  49,000 
ft.  per  second. 


91 
TABLE  NO.  42. 

WIND  IN  DAKOTA. 

Average  daily  and  hourly  Wind  Velocity  for  9  years  from  1882 
to  1891,  inclusive,  at  Huron,  S.  D.,  by  Sam.  W.  Glenn,  U.  S. 
Weather  Bureau. 


Month. 

Average  daily 
velocity,  miles. 

Average  hourly 
velocity,  miles. 

January 

232.5 

9.7 

February 

242.6 

10.1 

March 

239.9 

1U.O 

April 

274.8 

13.1 

May 

265.7 

11.1 

June 

238.6 

9.9 

July 

220.2 

9.2 

August 

217.5 

9.0 

September 

254.0 

10.6 

October 

244.7 

10.0 

November 

227.0 

9.5 

December 

224.2 

9.3 

Average  hourly  velocity  for  9  years  =  10.1  miles. 

TABLE  NO.  43. 
KAIN  IN  DAKOTA. 

Total  Rain  Fall  by  months  as  recorded  at  Huron,  S.  D.,  from  1881  to  1*92 
by  S.  \V.  Glenn,  L).  S.  Weather  Bureau. 


Year.  Jan  Fob 

Mch  Apr. 

May 

June  |  July  I  Aug.  i  Sep. 

Oct.  Nov. 

Dec. 

Tot'l 

ISM    1  

3.58    6.31    3.11 

2.10i     .45 

.06 

1882 

.14    .25 

.80 

4.18 

4.50 

5.86 

5.83    1.44      .86 

3.:57 

.61 

.23  28.12 

1883 

.17    .47 

.42 

2.14 

4.45 

4.33 

5.20    1.77    1.68 

1.96 

.05 

.61  23.25 

1884 

.09;   .581.  53    2.70 

2.90 

3.18 

5.11    1.18    1.26 

1.52      .17 

.62  20.  s4 

1885 

.15 

.22 

.12    1.06 

5.20 

5.43 

4.52    3.M)    2.61 

.98 

1.50 

.10  25.78 

1888 

.48 

.16 

.62 

3.52 

1.58 

1.90 

1.60    5.62!  1.59 

1.26 

1.18 

.74 

20.25 

is>7 

.:« 

1.11 

.64 

3.72 

1.88 

8:W 

4.96 

6.13      .15 

.79 

.25 

2.09 

25.54 

1888 

.78 

.52 

1.22 

.88 

4.98 

1.10 

3.11    3.46      .19 

.29 

.34 

.18 

17.05 

1889 

1.28 

.93 

.19 

3.41 

3.04 

1.04 

3.51 

.68    3.89 

.55 

.16 

1.53 

20.17 

1890 

.66 

.18 

.32 

.64 

2.88 

5.87 

1.41 

.73      .32 

.61 

.38 

.68 

14.68 

1891 

.07 

1.32 

1.64 

3.  45 

.44 

8.  OS 

1.01 

1.43      .47 

.78      .94 

.54 

20.17 

Mean 

.41 

.57 

.72 

2.57 

3.14 

4.03  |  3.63 

2.96    1.46 

1.29      .55 

.67 

21.58 

1892  |  .28 

.70  |  1.11  |  5.90  |  6,03  |  4.00 

Total  in  6  months=18.02    . 

Read  carefully  the  note  on  the  next  page  with  reference  to  this  table. 
Read  it  twice— and  don't  forget  it. 

PRECIPITATION  FOR  FIRST  6  MONTHS 
DURING  THE  FOLLOWING  YEARS. 


I  1882 

11883 

1884 


15.73 
11.98 

10.98 
12.08 


8.26 
1887    11.16 
9.48 

9.87 


1891 
1892 
Av'g 


10.55 
15.00 
18.02 
12.10 


(See  also  table  No.  14.) 


92 

NOTE— As  to  precipitation  table  No.  43. 

This  table  of  rain-fall  has  much  interest  as  it  shows  the 
distribution  and  amount  of  our  rains  by  months  and  years. 

1882  was  Dakota's  "boom"  year  in  rain-fall,  as  in  other  re- 
spects, and  was  the  most  bountiful  on  record  in  consequence. 
1883— '85  and  '87  were  good  years,  while  1888— '89  and  '90 
were  years  of  almost  total  failure.  It  will  be  of  special  in- 
terest to  note  that  1889  and  1891  have  exactly  the  same  total 
rain-fall;  whereas  1889  was  a  year  of  drouth  and  failure, 
while  1891  was  a  year  of  phenominally  good  crops.  Note 
further  that  the  record  of  1891  followed  a  record  of  but  14.68 
in  1890;  whereas  the  equal  record  of  1889  followed  a  record  of 
17.08  for  1838,  so  that,  so  far  as  the  records  for  the  two-year 
periods  are  concerned,  the  period  of  '89  and  '90  ought  to 
have  shown  better  results  than  the  period  of  '90  and  91. 

Note  still  further  that  the  rain-fall  of  1889  for  the  months 
from  January  to  July  was  but  13.36  inches  out  of  the  total  of 
20.17;  whereas  in  1891  the  rain-fall  for  these  months  was 
16.01  out  of  the  total  of  20.17.  Herein,  then,  lies  the  secret 
of  the  good  year  1891—  during  the  growing  months  of  1891 
there  was  a  rain  fall  of  2.65  inches  greater  than  during  these 
months  of  1889— the  totals  for  the  two  years  being  the  same. 

In  1889  the  rain  came  too  late,  while  in  1891  it  came  in  the 
proper  season . 

A  valuable  lesson  may  therefore  be  drawn  from  the  table 
— it  is,  that  the  2  or  3  inches  of  timely  rain  in  1891  saved  Da- 
kota from  a  fourth  year  of  failure,  and  enriched  the  people 
at  the  rate  of 

OVER  $5,000,000  PER  INCH. 

There  is  the  record!    There  is  the  lesson! 

From  this  draw  the  further  lesson  as  to  the  true  value  of 
the  water  of  a  well  the  distribution  of  which  you  have  in 
your  absolute  control  both  as  to  the  quantity  and  the  time 
when  it  shall  be  used. 

If  this  lesson  alone  is  well  learned  by  a  few  then  will  that 
one  table  have  made  this  little  book  well  worth  the  cost  of 
publishing. 


First 

Last 

Temperature. 

Days 

Year 

Frost 

Frost 

Highest 

Lowest 

Clear. 

Fair 

Cloudy 

Rain 

*1881 

Sept  15 

95  6° 

—  6° 

62 

81 

41 

66 

1882 

"      20 

May  22 

93.7 

-20 

113 

171    i        81 

96 

1883 
1884 
1885 

July  17 
Sept  11 

April  30 
May  13 
June  8 

99.2 
95.9 

98.2 

—32 

-38 
—33 

110 
139 
129 

168 
155 
164 

87 
72 

72 

115 
111 

95 

1886 

Aug.  31 

May  6 

103.6 

—33 

121 

180 

64 

118 

1887 
1888 

Sept.  15 

'    3 
<  18 

99.2 
101.7 

—43 

-36 

130 
141 

162 
142 

73 
83 

114 
95 

1889 

"        5 

'    2 

104.0 

—30 

133 

143 

89 

92 

1890 

Aug.  22 

1  15 

103.0 

-28 

151 

150 

64 

90 

1891 

•'      23 

'  16 

97.0 

—24 

135 

136 

94 

92 

Records  from  Huron,  S.  D.,  Signal  Station. 
*From  July  1st  1881. 


93 

TO  MEASURE  THE  HEIGHT  OF  A  STREAM. 

The  following  method  will  enable  any  one  to  easily  and 
quickly  measure  the  exact  height  of  the  stream  thrown  out 
by  a  well,  without  the  use  or  instruments  or  of  tables  of 
tangents. 

Referring  to  figure  11  let  W  be  a  well  and  EF  the  stream 
thrown.  Carefully  measure  off  a  distance  of  say  100  feet 
and  drive  a  stake  8,  to  the  level  of  the  pipe  if  possible. 
Drive  another  3  or  4  feet  nearer  and  across  the  top  nail  a 
piece  of  board  B;  which  set  level.  Measure  off  AC  =  5  feet 
(or  any  other  amount)  and  nail  the  stick  H  to  this  mark, 
and  at  right  angles  to  AC.  Now  look  over  the  point  of  the 
board  at  A  and  have  some  one  mark  on  the  stick  H  a  point 
D  in  line  with  E  the  top  of  the  stream  EF.  Measure  the 
length  CD,  then  may  the  height  EF  be  found  by  simple 
proportion. 

Example.  AF  =  100  ft.  AC  =  5  ft.  CD  =  4  ft.  then, 
AC  :  AF  : :  CD  :  FE  or  5  :  100  : :  4  :  (required  height) 

100  x  4  =  400,  400  -s-  5  =  80  ft.  =  height  of  stream  EF. 

If  the  horizontal  line  AF  will  not  strike  the  top  of  the 
pipe,  as  at  Y,  measure  the  distance  YZ  and  subtract  it  from 
the  total  height  found. 

Although  a  rough  method  it  is  an  easy  one  and  sufficient 
accuracy  may  be  obtained.  If  this  is  done  by  all  wells,  while 
throwing  streams  of  different  sizes,  and  a  record  made  of 
the  results  it  will  be  a  vast  improvement  on  the  guess-work 
so  freely  indulged  in  heretofore. 

Fig.  11. 
Method  of  measuring  height  of  a  stream. 


e 


4' 

&•• 


/op' 


(See  also  page  147.) 


25         Xongitufle    West  23          f- •••- 


From  Harper's  Magazine. 


Copyright,  1889,  by  Harper  &  Brothers. 


FIG,  12.    WEATHER  MAP  OF  NORTH  AND  SOUTH  DAKOTA. 

By  permission  of  Messrs.  Harper  &  Brothers. 

Showing  isothermal  lines  and  areas  of  varying-rainfall.  It  will  be 
seen  that  nearly  all  of  the  agricultural  section  of  both  states  has  a 
range  of  rainfall  of  from  i$ — 20  inches.  This  area  should  extend 
farther  to  the  South  than  shown  on  the  map. 


Harper's  Magazine.— Copyright,  1889,  by  Harper  &  Brother*. 


Fig.  13-     View  of  Brick- Yard  Well  at  Yankton,  S.  D. 

From  photograph  by  L.  Janousek,  Yankton. 
By  permission  of  Harper  and  Brothers. 

Depth  =  595  feet.    Size  of  pipe  =  6  inches. 

Pressure  =  48  to  57  Ibs.  per  square  inch. 

Volume  =  1620  to  2000  gallons  per  minute. 

Location,  on  top  of  the  Missouri  river  bluffs. 

Use,  for  power.    Cost,  about  $3,000. 

The  view  as  taken  showed  the  well  throwing  a  6  inch  stream  about  6  feet 
above  the  top  of  a  20  foot  stand-pipe.  This  well  is  one  of  a  number  of 
large  wells  in  the  southern  portion  of  South  Dakota  having  a  compara- 
tively low  pressure  and  very  large  volume. 


96 

RESERVOIRS. 

In  the  western  states  where  irrigation  by  water  taken  from 
streams  is  the  rule,  and  irrigation  by  well  waters  the  excep- 
tion, the  waters  are,  in  most  cases,  impounded  at  some  place 
near  their  head  waters  where  the  topography  is  such  as  to 
admit  of  the  construction  of  a  dam  which  will  create  a  res- 
ervoir in  the  valley  wherein  are  stored  the  waters  of  the 
freshet  season  for  use,  many  miles  away,  during  the  season 
of  drouth.  {Such  vast  engineering  works  can  only  be  entered 
upon  by  corporations  possessing  vast  capital,  for,  in  some 
cases,  the  dam,  with  flumes  and  ditches  to  convey  the  water 
to  the  irrigated  districts,  has  cost  over  a  million  dollars. 

The  general  government  has  already  provided  for  the  lo- 
cation, survey  and  reservation  of  all  sites  on  the  public  do- 
main where  dams  and  reservoirs  may,  to  advantage,  be  lo- 
cated in  the  future,  and  wise  restrictions  have  been  thrown 
around  corporations  securing  such  sites  so  as  the  best  to  pro- 
tect the  individual  comsumers  from  corporate  exactions 

Vast  tracts  of  the  finest  land  in  the  world  lie  undeveloped 
and  barren  because  the  necessary  capital  has  not  yet  been 
found  to  improve  it  by  flrst  constructing  a  dam  and  creat- 
ing a  reservoir  for  the  storage  of  the  necessary  water. 
•    IN  DAKOTA  how  different  is  all  this? 

There  is  not  in  the  state  a  reservoir  site  worthy  of  the 
name  and  no  money  need  be  expended  on  great  engineering 
works  for  the  storage  of  water.  Nor  is  there  a  stream  that 
can,  to  advantage,  be  dammed.  The  Dakota  reservoir  will 
rarely  if  ever  exceed  10  acres  in  area  and  in  place  of  one  cov- 
ering many  miles  there  may  be  several  small  ones  on  one 
mile. 

When  artesian  irrigation  was  lirst  agitated  it  was  the 
popular  belief  that  the  well  waters  might  be  run  directly 
into  the  ditches  and  thence  distributed;  but  no  thought  was 
given  to  tlie  fact  that  thereby  the  service  of  a  well  of  but 
moderate  volume  would  be  very  limited,  for  the  water  flow- 
ing within  any  given  time  would  be  insufficient,  within  that 
time,  to  cover  any  considerable  area. 

If,  however,  the  waters  could  be  stored  in  a  reservoir  dur- 
ing such  periods  as  it  was  unnecessary  to  apply  any  to  the 
land  then  when  water  was  needed  over  a  broad  area,  and 
within  a  brief  period  of  time,  the  accumulated  store  could  be 
made  to  do  service  which  the  well  alone  could  not  do  in  the 
same  time.  The  necessity  for  small  storage  reservoirs  being 
thus  apparent  they  become  as  much  a  part  of  every  irriga- 
tion plant  as  the  well  itself.  In  fact  if  the  land  under  ser- 
vice of  any  particular  well  is  quite  rolling  it  may,  and  in 
many  cases  will,  be  necessary  to  have  two  or  more  small  res- 
ervoirs on  the  farm  in  order  to  secure  the  best  service  to  the 
land  and  the  most  economical  storage  and  distribution. 

Reservoirs  being  necessary,  how  and  where  shall  thev  be 
built? 


97 
LOCATION. 

The  highest  points  will,  of  course,  be  the  natural  sites  for 
reservoirs  but  the  land  may  lay  so  as  to  make  it  not  only 
better  but  cheaper  not  to  locate  the  reservoir  on  the  highest 
point.  Such  cases  will  be  few  and  the  conditions  in  mind 
will  in  all  such  cases  be  apparent  to  one  on  the  ground.  If 
a  tract  of  land  is  divided  into  two  or  more  parts  by  a  gully 
or  depression  of  any  extent  it  may  be. best  in  such  case  to 
have  two  or  three  smaller  reservoirs,  one  on  each  tract  or 
division  of  the  land.  If  but  one  large  reservoir  were  built 
the  other  tracts  or  elevations  would  have  to  be  served  from 
flumes  which  would  be  larger  and  more  expensive  than  one 
sufficient  to  feed  the  reservoir  alone,  and  they  might,  at  the 
critical  time,  fail  to  do  proper  service  by  reason  of  adverse 
winds  or  other  causes  thereby  causing  more  loss  than  a 
reservoir  would  cost. 

In  ordinary  cases  the  proper  site  for  a  reservoir  may  be  se- 
lected by  a  farmer  without  the  aid  of  an  engineer  but  where 
any  doubt  exists  as  to  the  choice  of  locations  then  no  chances 
should  be  taken  and  the  services  of  one  competent  to  judge 
should  be  secured. 
FORM. 

In  most  cases  the  circular  form  will  be  adopted  because 
the  greatest  area  is  enclosed  by  a  given  amount  of  bank. 
Occasional  departures  from  this  form  will  be  necessary  by 
reason  of  the  lay  of  the  land. 

Only  the  cicular  form  will  be  considered  in  the  tables. 
SIZE. 

The  matter  of  size  will,  in  a  few  cases,  be  governed  by  the 
land  but,  as  a  rule,  the  service  to  be  rendered  by  the  waters 
stored  will  govern.  If  a  township  well  is  to  be  provided 
with  storage  then  the  volume  of  the  well  should  be  deter- 
mined in  order  to  know  how  small  a  reservoir  would  suffice 
not  only  to  give  service  to  the  area  to  be  irrigated  but  also 
to  hold  all  the  water  the  well  will  supply  within  the  longest 
time  it  could  be  permitted  to  run  without  allowing  the  wa- 
ter in  the  reservoir  to  be  drawn  off.  This  would  give  all  the 
necessary  storage  capacity  without  any  waste  of  money  in 
making  it  larger  than  needed. 

Since  most  wells  throw  over  500  gallons  per  minute  the 
time  of  impounding  could  not  be  long  except  with  a  very 
large  reservoir.  Table  No.  37  taken  in  connection  with  ta- 
bles 47  and  48  will  quickly  supply  all  needed  information  in 
this  connection.  From  them  it  will  be  seen  that  a  500  gallon 
well  will  fill  a  10-acre  reservoir  seven  feet  deep  every  30  days, 
&c.,  &c.  Where,  as  in  case  of  a  township  well  which  will  be 
used  to  serve  several  farmers,  the  volume  used  will  be  large 
the  storage  capacity  should  be  as  large  as  economy  will  war- 
rant and  each  consumer  might  to  his  own  advantage  be  sup- 
plied with  a  sub-reservoir.  In  case  of  special-service  or  sub- 
reservoirs  which  are  designed  to  serve  only  a  limited  area  as 
for  example,  a  knoll  of  10  or  15  acres  then  the  water  to  be 


98 

used  on  that  area  alone  should  be  estimated  and  storage  area 
provided  only  sufficient  for  that  volume,  allowance  being 
made  for  seepage,  evaporation  and  waste.  Thus,  assume  a 
field  of  10  acres  to  be  supplied  by  a  sub-reservoir  and  volume 
sufficient  provided  to  flood  the  land  6  inches;  what  would  be 
the  size  of  reservoir  required  if  the  water  be  given  a  depth 
of  5  feet  in  the  reservoir  V  Table  34  or  table  21  gives  the  cu- 
bic feet  of  water  required  to  flood  10  acres  6  inches  deep  as 
217,800.  Table  29,  under  head  of  water  5  feet  deep,  shows  at 
a  glance  that  a  reservoir  of  1^  acres  will  hold  this  volume 
and  enough  more  to  cover  all  waste.  Table  45  gives  the 
diameter,  circumference  and  area  of  this  reservoir. 

These  suggestions  will  show  the  importance  of  duly  con- 
sidering the  elements  of  volume  of  well,  time  it  may  flow, 
area  to  be  served,  &c.,  in  the  laying  out  of  a  reservoir  for 
either  general  or  special  service.  The  depth  of  water  in  the 
reservoir  will  always  enter  into  the  consideration. 

Where  any  considerable  volume  is  required  it  will  be  best 
to  have  the  depth  in  excess  of  4  feet,  first,  because  if  the  wa- 
ter is  deeper  the  reservoir  will  occupy  less  ground  for  a  given 
capacity;  second,  the  evaporation  will  be  less,  the  exposed 
area  being  less,  and  the  waste  from  seepage  will  be  less; 
third,  the  wash  of  the  banks  will  be  less  because  the  wind 
will  have  less  sweep  over  the  surface. 
Table  of  sizes. 

Table  No.  45  shows  the  diameters,  circumferences,  and 
areas  in  sq.  ft.  of  reservoirs  from  %  acre  to  10  acres,  for 
each  %  acre,  and  explanation  follows  as  to  calculating  the 
elements  for  otht  r  sizes. 
LAYING  OUT. 

The  size  haying  been  determined  the  staking  out  follows. 
If  the  reservoir  is  to  cover  a  given  area  the  whole  bank  will 
be  within  that  area  and  the  foot  of  the  outer  slope  will 
bound  the  given  area.  If  the  area  is  to  exclude  the  bank  the 
foot  of  the  inner  slope  will  bound  the  area.  If  the  water  is 
to  cover  a  given  area  then  the  high  water  line  or  the  point 
half  way  down  the  bank  therefrom  will  bound  the  given  area. 
Or  the  area  may  be  bounded  by  the  center  line  either  of  the 
whole  bank  or  of  the  top  of  the  bank. 

Usually  these  considerations  will  not  be  of  much  import- 
ance, but  in  case  of  joint  ownership  or  of  contracting  for 
the  construction  they  may  be  important  and  should  then  be 
clearly  understood  and  carefully  specified .  In  staking  out 
it  will  be  best,  for  the  convenience  ot  graders,  to  drive  stakes 
on  the  outer  and  inner  lines  of  the  bank.  The  line  of  the 
top  follows  as  a  result  of  the  slopes. 

The  measurement  may  be  made  with  a  measured  wire 
one  end  of  which  is  fastened  or  held  at  the  center  while  the 
outer  end  is  carried  around  and  stakes  driven  at  convenient 
distances  along  the  circle.  If  wire  cannot  be  had  then  rope 
or  even  binding  twine  will  answer  the  purpose. 


If  the  land  is  uneven  or  covered  with  stubble,  corn  stalks, 
growing  grain  or  other  obstructions  which  prevent  swing- 
ing the  wire  or  line  around  the  center  point  then  two  per- 
sons may  manage  the  wire  or  line  as  follows.— A  holds  one 
end  at  the  center  while  B  drives  stakes  at  the  north  points; 

(At  both  the  inner  and  outer  slopes  of  the  banks.) 

both  then  walk  south  across  the  circle  until  B  reaches  the 
center  when  A  drives  the  south  stakes;  they  then  walk  back, 
B  turning  a  little  to  the  east  or  west,  until  A  comes  again 
to  the  center  while  B  drives  stakes  at  the  outer  end;  A 
then,  as  before,  walks  straight  across  the  circle  and  drives 
other  stakes.  Repeat  this  until  the  circuit  of  the  circle  has 
been  made  and  all  the  stakes  set .  The  result  is  the  same 
but  the  walking  a  little  more.  Any  farmer  can  thus  lay 
put  his  own  reservoir,  if  need  be,  in  an  hour's  time  and  do 
it  as  well  as  it  could  be  done  by  an  engineer  at  an  expense 
to  the  farmer  of  $5  to  $10.  The  outlines  having  been  staked 
out,  and  the  stakes  numbered,  the  levels  should  be  taken  to 
determine  the  height  of  the  bank  at  each  stake.  If  the 
ground  is  not  fairly  level  the  stakes  will  have  to  be  set  in 
or  out  to  give  the  proper  base  line  according  to  the  length 
of  the  slope. 

Where  the  ground  is  comparatively  level  any  farmer  can 
do  his  own  leveling  not  only  for  reservoirs  but  for  ditches, 
but  where  it  is  rolling  the  services  of  an  engineer  should  be 
secured  as  a  measure  of  economy.  Better  to  pay  for  having 
the  work  properly  done  by  responsible  parties  than  to  do  it 
wrong  and  then  be  obliged  to  have  it  done  over  again. 

See  notes  on  leveling,  page  128  and  following  pages. 
THE  BANKS. 

The  banks  should  be  constructed  of  as  firm  earth  as  pos- 
sible in  order  to  give  strength  and  prevent  percolation  and 
washing,  and  they  should  be  thrown  up  by  drag  scrapers 
which  results  in  a  more  solid  and  firmly  packed  bank  than 
can  be  made  by  the  use  of  wheel  scrapers  or  graders  unless 
the  work  with  the  latter  be  properly  done.  (See  embank- 
ments and  footings— under  head  of  Ditches.)  The  outer 
slope  may  be  one  of  1^  horizontal  to  1  vertical.  The 
breadth  of  the  top  will  depend  upon  the  height  and  strength 
required.  Most  reservoirs  will  be  9  feet  or  less  in  height 
and  for  such  heights  a  width  of  top  of  5  feet  will  be  suffic- 
ient. Where  the  bank  exceeds  9  feet  in  height  an  additional 
foot  in  width  may  be  added  for  each  2  feet  of  additional 
height,  the  slopes  remaining  the  same. 

Fig.  14,  on  the  next  page  shows  in  sectional  diagram  the  inner  slopes  of 
banks  from  1  ft.  to  14  ft,  high  and  with  slopes  of  2  to  1.  The  horizontal 
lines  indicate  the  water  levels  and  the  diagonal  lines  the  slopes  of  the 
banks.  The  upper  horizontal  line  of  figures  indicate  the  distances  of  the 
foot  of  the  banks  from  the  top  (measured  horizontally ;)  and  the  lower 
line  of  figures  the  amount  the  diameter  of  the  reservoir  is  reduced  by 
banks  of  the  different  heights.  Thus,  if  the  bank  is  8  feet  high  and  the 
water  4  ft.  deep  the  shore  line  will  be  at  A  and  the  area  of  the  water  sur- 
face will  have  a  diameter  21  feet  less  than  that  of  the  reservoir  (measured 


100 


:>  center  line  of  top.)  To  get  the  volume,  take  the  diameter  half  way 
own  the  bank,  at  C,  which  is  29  ft.  less  than  the  total  diameter,  and  pro- 
sed as  explained  in  the  tables.  The  further  use  of  the  diagram  will  be 


Kla.  14. 

Slope  Diagram  for  Banks  of  Reservoirs. 


6      a      TO     is      14. 

FECT     TO   FOOT     OF     BANK  . 

B        13        /?      ai       25       29      3d     3?      41      45 
0/AM£T£Ft   OF  f?£S.  TO  BE  #eOUC£D    BY—  FT. 

Table  No.  44  shows  the  cross  sections  of  banks  from  3  ft.  to  10  ft.  high ; 
with  area  of  cross  sections  and  cubic  yards  of  earth  per  lineal  foot  and 
per  100  feet. 

This  table  will  be  of  use  to  contractors  and  graders. 

To  find  the  cubic  contents  of  a  bank  X  the  area  of  the  cross  section  by 
the  length  of  the  bank  in  feet  and  then  divide  by  27.  Thus,  in  first  exam- 
ple given  in  the  table,  the  area  of  the  cross  section  =  6  X  10  =  60  )  Total 

20  X    5  =  100  \  =  235 
15  X    5  =    75)sq.  ft. 

this  X  1656  (the  circumference  of  a  6  acre  reservoir)  =  389,160  cubic  feet 
which  -!-  27  =  14,413  cu.  yds. ;  by  table— 870.37.  the  cu.  yds.  in  100  ft-  X  16.56 
=  14.413  the  same  as  by  the  other  and  longer  method. 

WASHING  OF  BANKS. 

The  washing  down  of  the  banks  by  the  waves  in  the  reservoir  is  a  mat- 
ter of  much  importance  and  yet  little  can  be  said  as  to  the  best  means  of 
preventing  it.  Where,  as  is  the  case  in  some  sections,  there  are  plenty  of 
stone  the  water  line  may  be  partially  protected  by  riprapping  with  them 
but  this  involves  a  large  amount  of  labor.  In  most  sections  of  the  state 
there  are  no  stone  so  other  means  must  be  used.  In  sections  near  the 
James,  or  other  rivers,  along  which  willows  grow  these  willows  may,  at 
but  little  expense,  be  transplanted  in  the  banks  where  they  will  form  a  self 
maintaining  protection.  Nor  can  this  expedient  be  practiced  by  but  few. 
The  tough  prairie  sods  taken  from  the  surface  of  the  ditch  may  be  laid 
aside  and"  be  afterward  laid  along  the  water  line.  This  has  been  tried  and 
has  worked  well  and,  although  much  labor  is  involved  it  probably  re- 
mains the  best  for  general  use.  Where  gravel  may  be  had  a  shore  line  may 
be  covered  with  it  thus  forming  a  natural  water  break.  In  some  cases  it 
may  be  best  to  construct  a  break-water  of  plank  sharpened  and  driven  into 
the  bank  or  laid  to  posts  set  in  the  bank.  The  steeper  the  bank  the  great- 
er of  course  will  be  the  displacement  of  the  earth  by  wave  action. 
Outlets  and  Gates-See  P.  107. 


101 


TABLE    NO,lT44.ACRO|SA|ECTIONcScOF RESERVOIR    BANKS 


SECTIONS     Area  of 

cross 
section 
Sq.  ft. 


41* 


47' 


33' 


2.35 


189. 


CuYds 
erf  t  of 
bank 


Cu.Yds. 

perf  t  of  per  100  ft. 
of  bank. 


s.  70:57 


7.0 


870.37 


700.0 


122.5 


93. 


48. 


31.5 


44. 


28.5 


5.6296       562.96 


4.5370 


3.4444 


2.5925 


1.7777 


1.6296 


1.0505 


453.70 


344.44 


259.25 


177.77 


116.66 


162.96 


105.05 


102 

TABLE  NO.  45.      RESERVOIR  TABLE. 
Diameters,  Circumferences  and  Areas  in  square  ft.  of  reser- 
voirs from  y%  acre  to  10  acres  in  area  —  advancing  by  3^  acre. 

New. 


Area  in 
Acres. 

Diameter 
in  feet. 

Circmuference 
in  feet. 

Area  in  Square 
feet. 

Ys 

83+ 

261 

5455 

M 

118— 

371 

10890 

n 

167— 

525 

21  780 

M 

204— 

641 

32  670 

235— 

738 

43560 

M 

263+ 

826 

54450 

1 

288+ 

905' 

65340 

M 

312— 

980 

76230 

2 

333+ 

1046 

87120 

M 

353+ 

1109 

98010 

« 

372+ 

1169 

108900 

M 

391— 

1228 

119  790 

3 

408— 

1282 

130680 

M 

425— 

1335 

141  570 

it 

441— 

1385 

152  460 

M 

456+ 

1433 

163  350 

4 

471+ 

1480 

174  240 

M 

486— 

1527 

185  130 

% 

500— 

1571 

196  020 

M 

513+ 

1612 

206  910 

5 

527— 

1656 

217800 

M 

540— 

1696 

228690 

iz 

552+ 

1734 

239  580 

M 

565— 

1775 

250  470 

6 

577— 

1813 

261  360 

589— 

1850 

272  250 

M 

601— 

1888 

283  140 

M 

612— 

1923 

294030 

7 

623+ 

1957 

304  920 

M 

634+ 

1992 

315810 

}2 

645— 

2026 

326700 

i 

656— 

2061 

337  590 

8 

666+ 

2092 

348  480 

M 

676+ 

2124 

359  370 

i^ 

687— 

2158 

370  260 

M 

697— 

2189 

381  150 

9 

707— 

2221 

392  040 

M 

716+ 

2249 

402  930 

M 

726— 

2281 

413  820 

M 

735+ 

2309 

424710 

10 

745— 

2340 

435600 

NOTE — In  the  above  table  the  diameters  and  circumferences  are  taken  to 
the  nearest  foot.  The  area  in  square  feet  is  correct  for  the  given  areas  in 
acres.  The  signs  of  +  and  —  after  the  diameters  indicate  whether  the  di- 
ameters given  are  too  large  or  too  small.  Thus,  83  +  indicates  that  a 
fraction  of  a  foot,  less  than  l/2 ,  must  be  added  to  83  to  give  the  true  diam- 
eter ;  and  118  —  indicates  that  a  fraction  less  than  %  foot  must  be  taken 
from  118  to  give  the  true  diaineter ;  83  is  therefore  a  little  too  small  and 
118  a  little  too  large —  less  than  V£  foot  in  each  case.  See  explanation  on 
next  page. 


103 

Explanation  as  to  table  45.  Table  No.  45  is  constructed 
from  table  72;  the  areas  in  square  feet  having  first  been  cal- 
culated. The  area  in  sq.  ft.  of  a  5  acre  res.  being  217,800 
enter  table  72  in  the  column  of  areas  and  find  2181.28  as  the 
area  of  a  circle  whose  diameter  is  52.7  and  circumference 
165.56.  This  tabular  area  agrees  most  nearly  with  the  given 
area  in  sq.  ft. 

Therefore,  for  a  circle  of  527  ft.  diam.  the  circumference 
would  be  1655.6  ft.  (decimal  point  ONE  place  to  the  right.) 
and  the  area  218,128.  (decimal  point  TWO  places  to  the  right.) 
This  area  corresponds  most  nearly  to  the  given  area  and 
hence  the  diameter  and  circumference  are  the  ones  most 
nearly  corresponding  to  the  given  area.  If  diameter  is  less 
than  100  the  area  and  circumf.  may  be  taken  directly  from 
the  table.  If  diameter  is  more  than  100  and  less  than  1000 
enter  the  table  72  and  from  the  first  column  take  the  whole 
number  and  decimal  corresponding  to  the  given  diameter; 
then,  for  the  area,  move  the  decimal  point  TWO  places,  and 
for  the  circumference  ONE  place,  to  the  right.  Example, 
required  the  circumference  and  area  of  a  circle  or  reservoir 
having  a  diameter  of  472  ft.  ?  In  table  72  opposite  47.2  (473) 
find  circumf.  =  1482.8  and  area  =  174  974.1  [The  decimal  point* 

having  been  moved  as  above  described-^       The  area  in  acres  IS  found 

by  dividing  the  area  in  sq.  ft.  by  43560. 

If  either  the  diameter,  circumf.  or  area  in  sq.  ft.  or  acres 
be  given  all  the  other  elements  may  thus  be  found  from 
table  72. 

EVAPORATION  AND  FILTRATION. 

Evaporation  is  the  greatest  during  warm  or  windy  weath- 
er; greater  in  shallow  than  in  deep  water  and  greater  in  run- 
ning than  in  still  water.  The  evaporation  from  a  ditch  or 
reservoir  during  June,  July  and  Aug.  will  rarely  exceed  .3 
to  ,4  inch  per  day.  During  the  remaining  months  the  aver- 
age will  be  about.  I  inch  making  for  the  year  from  3  to  5 
feet  of  loss  by  evaporation.  To  the  loss  by  evaporation  must 
be  added  the  loss  by  seepage  or  filtration  either  into  the 
earth  or  through  the  banks.  The  amount  of  seepage  through 
the  banks  will  depend  not  only  upon  the  character  of  the 
soil  of  which  they  are  made  but  also  upon  the  solidity  with 
which  they  have  been  thrown  up.  80  with  the  seepage  into 
the  earth.  If  the  soil  is  of  soft  loam,  sand  or  gravel  the  per- 
centage of  loss  will  be  much  greater  than  if  the  sub-soil  is  of 
clay  or  hard-pan. 


ed  reservoir  on  average  ground  may  be  as 
after  the  reservoir  has  been  in  use  for  a  s 
show  the  approximate  volume  of  loss  per 
different  areas. 

TABLE  NO.  46. 

Showing    loss    in    Reservoirs 
from  Evaporation  and  Filtration. 
Approximate  only. 

>sumed  to  be  about!  inch  per  day 
eason.    The  following  table  will 
day  in  gallons  from  reservoirs  oi 

Area 
acres 
i~ 

2 
3 
4 
5 

Loss  in  j  Area 
Gallons,  'acres 
~~2710(r  1      6~~ 
54300           7 
81400    1      8 
108600    i      9 
135700     i     10 

Loss  in 
Gallons. 

162000 
190000 
217000 
244000 
271000 

104 


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105 
TABLE  NO.   48. 


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106 


TABLE  NO.  49. 

COST  OF  RESERVOIRS. 

With  banks  4,  6  and  8  feet  high,  and  at  rates  of  6  and  8  cents 
per  cubic  yard  for  moving  earth.  (To  cost  of  embankment 
add  cost  of  outlets,  gates,  protection  for  banks,  etc.) 


(M  i-i  t^  I>  O  ^  <M  (M 
COtr-L—  ^^i—(QO^f 
CC  •  ^  lO  ^  t^  QO  QO  3i 


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i-H^OLOCi 


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QO(MCCOi(M^I>- 

H  hH  CM  CM  CM  CO  CO  CO  C 


NOTE— It  is  assumed  that  the  price  of  moving  earth  will 
be  from  6  to  8  cents  per  yard  at  which  rate  (8c)  most  of  the 
subcontract  work  on  Dakota  Ry.  grades  has  been  let,  the 
lesser  rate  of  6  cents  has,  in  some  cases,  been  paid.  If  the 
cost  is  desired  for  an  embankment  of  any  other  size  or  cross 
section  the  length  may  be  taken  directly  from  table  45,  the 
cross  section  from  table  44  and  the  cubic  yards  then  quickly 
calculated  and  multiplied  by  the  price  agreed  upon,  in  order 
to  get  the  total  cost.  This  table  will  answer  most  purposes 
and  will  be  of  value  for  ready  reference. 


107 


rmitimu'd  from  page  100. 

OUTLETS  AND  GATES. 

OUTLETS.  The  outlets  or  culverts  through  the  banks  to 
the  main  ditches  should  be  set  before  the  bank  is  built  and 
with  refeference  to  the  location  of  the  ditches.  The  size  of 
the  outlet  will  be  governed  by  the  amount  of  water  to  be  de- 
livered to  the  ditch.  If  the  ditch  is  small  or  short  the  size 
may  be  smaller  than  for  a  large  or  long  ditch.  In  the  latter 
case  make  the  outlet  large  enough  to  deliver  the  requisite 
amount  of  water  at  a  velocity  not  so  great  as  to  wash  the 
banks  of  the  ditch.  The  outlets  may  be  made  of  plank  or  of 
sewer  pipe,  the  latter  being  especially  good,  but,  in  most 
cases,  not  so  readily  obtainable.  The  earth  should  be  well 
tamped  about  the  box  or  pipe  in  order  to  make  a  water  tight 
joint. 

By  reason  of  the  difference  in  sizes  of  the  outlets,  the  dif- 
ference in  length  through  banks  of  different  breadths,  and 
with  the  difference  in  the  head  due  to  constant  lowering  of 
the  water  in  the  reservoir,  and  the  different  methods  of  con- 
structing the  outlets,  no  precise  data  can  be  given  as  to  the 
relative  discharging  capacities  of  different  sizes  of  outlets 
but  the  following  table  will  give  the  approximate  volumes 
in  cubic  feet  per  minute  discharged. 

TABLE  NO.  50. 


FLOW  OF  WATER  FR  OM  RESERVOIRS. 


New. 


Head  of 
water 
in  feet. 

Outlet 

12X12 
inches 

Outlet 
12X24 
inches 

Outlet 
12X36 
inches 

Outlet 
24X24 
inches 

Outlet 
24X36 
inches 

2 
3 
4 
5 
6 

400 
500 
575 
650 
720 

800 
1000 
1150 
1300 
1440 

1200 
1500 
1725 
1950 
2160 

1600 
2000 
2300 
2600 

2880 

2400 
3000 
3450 
3900 
4320 

Cubic  ft. 
per  min. 

GATES.  The  gates  should  be  set  at  the  the  inner  end  of 
the  outlets  and  a  plank  walk  built  from  the  top  of  the  bank 
leading  out  over  the  water  to  a  point  over  the  gate  in  order 
that  the  gate  may  be  lifted.  In  construction  the  gate  is 
most  simple;  any  farmer  or  carpenter  being  competent 
to  make  them.  A  tightly  fitting  slide  over  the  end  of  the 
box  or  pipe  outlet  being  all  that  is  necessary  to  shut  off  the 
water.  The  gate  may  be  raised  or  lowered  by  a  stick  of  2x4 
bolted  to  the  front  of  the  gate  and  leading  up  through  slides 
or  guide  holes  in  the  end  of  the  walk.  Simple  means  too 
may  be  provided  for  fastening  the  gate  either  up  or  down. 
The  pressure  of  the  water  against  the  gate  will  keep  it  in 
position  and  preserve  a  tight  joint  if  the  sliding  surfaces 
have  been  properly  dressed  or  surfaced.  Guides  should  be 
provided  in  the  sliding  supports  so  as  to  make  sure  that  the 
gate  will  return  to  its  seat  when  it  is  desired  to  lower  it. 
Modifications  of  detail  are  many  and  will  suggest  themselves 


108 

to  any  one  as  the  conditions  of  the  work  or  the  setting  may 
require. 


Fig.  16  shows  a  simple  and  common  form  of  gate. 


Fig.  16. 

Simple  form  of 
gate.  aa=side  plank 
of  outlet  box.  66 
and  (•('  —  top  and  bot- 
tom plank  of  outlet 
box.  e  —  upright 
plank  supporting 
outer  end  of  walk. 
ff  =  guides  for  gate. 
s  =  space  in  which 


*      — 

*       gate  slides, 
h  =  hoisting 


timber. 


Sub  Reservoirs  and  Storage  Ditches. 

As  previously  stated  it  may  be  best  to  have  two  or  more 
reservoirs  on  the  same  farm  or  under  service  by  the  same 
well.  These  may  be  on  different  ridges  or  knolls  and  may 
be  directly  connected  with  the  well  or  with  each  other  by 
piping,  flumes  or  ditches.  A  sub  reservoir  may  be  provided 
to  receive  the  waters  elevated  from  lower  ditches  or  pools 
by  wind  mills  or  water  rams.  In  many  cases  storage  ditches 
will  be  necessary  to  give  proper  service  to  areas  at  a  consid- 
erable distance  from  the  well  or  reservoir.  A  storage  ditch 
is  merely  a  big  ditch,  or  one  made  higher  and  wider  than 
the  ordinary  main  ditch  so  as  to  hold  in  store  a  large  vol- 
ume of  water  ready  for  immediate  service  through  lateral 
ditches  to  the  adjacent  lands.  Such  a  ditch  or  canal  along 
a  quarter  line  might  better  serve  adjacent  farms  than  a  res- 
ervoir of  any  other  form,  or  if  located  along  the  top  of  a  nar- 
row ridge  where  a  large  circular  reservoir  would  be  imprac- 
ticable or  needlessly  expensive. 

For  the  volume  of  water  stored  a  storage  ditch  requires  a 
greater  cubic  capacity  of  embankment  and  hence  a  greater 
proportionate  cost  than  a  circular  reservoir;  but  the  econ- 
omy of  space,  the  lay  of  the  land  or  the  character  of  the  ser- 
vice to  be  rendered  may  more  than  compensate  for  the  in- 
creased proportionate  cost. 


109 

DISTRIBUTION  OF  WATER  BY  DITCHES, 
FLUMES  AND  PIPES\^C 

The  water  having  been  obtained  and  stored  the  next  e£n- 
sideration  is  as  to  its  conveyance  from  the  well  or  reservoir 
to  any  desired  place  and  then  its  distribution  over  the  land 
to  be  irrigated. 

The  distinctive  feature  of  the  great  irrigation  systems  of 
the  west,  and  of  other  countries,  is  the  great  length,  size, 
and  expense  of  the  ditches  and  flumes  necessary  to  convey 
the  water  from  the  storage  reservoirs  or  rivers  to  the  low- 
lying  irrigated  lands.  These  ditches  are  often  of  great  size 
and  extend  for  many  miles;  the  cost  reaching  tens  or  hun- 
dreds of  thousands  of  dollars.  Great  viaducts  of  masonry, 
or  trestles  of  timber  or  iron,  to  carry  the  canal  over  rivers 
or  valleys,  deep  cuts  along  the  mountain  sides,  flumes  sus- 
pended over  or  along  precipitous  canyons,  tunnels  through 
the  rock  hills,  and  enormous  dams  and  head  gates  are  feat- 
ures of  great  interest,  as  well  as  of  expense,  common  to 
the  distribution  of  irrigation  waters  in  regions  less  favored 
than  our  own. 

How  tame,  in  comparison,  will  be  the  means  of  distribu- 
tion on  the  Dakota  prairies  and  under  the  individual  sys- 
tem of  irrigation  by  wells.  Our  people  may  well  forego  the 
glory  of  being  the  possessors  of  world  renowned  works  of 
engineering  skill,  for  the  sake  of  the  greater  economy  and 
the  honorable  distinction  of  being  the  possessors  of  the 
largest  and  most  fertile  valley  in  America,  wherein  irriga- 
tion may  be  more  cheaply  inaugurated  and  maintained  than 
in  any  other  state* 

All  the  leading  features  of  other  systems,  such  as  dams, 
head-works,  main  canals,  pipe  lines,  viaducts,  &c.,  will  not 
be  known  here.  Probably  few  ditches  will  be  larger  than  10 
feet  at  the  bottom,  and  but  few  will  be  over  5  miles  in  length. 
Pipe  lines  will  be  small,  and  flumes  will  be  low  and  short. 
In  brief,  there  will  be  no  heavy  or  expensive  features  at- 
tached to  the  distribution  of  Water  in  this  prairie  country, 
and  hence  the  great  economy  of  an  irrigation  system  in 
Dakota. 

The  result  sought  by  all  systems  is  the  bringing  of  water 
to  the  land. 

While  it  may  sound  well,  or  arouse  in  one  the  spirit  of 
pride,  to  say  that  we  have  the  largest  dam,  the  largest  or 
the  longest  ditch,  the  longest  tunnel,  or  the  highest  flume 
in  the  world,  it  is  a  distinction  the  wary  capitalist  will  will- 
ingly forego  for  the  more  humble  statement  that,  for  a 
given  outlay,  we  have  under  water  a  larger  number  of  acres 
than  can  be  shown  any  where  else.  This  will  be  the  pride 
of  the  Dakota  irrigator.  He  will  point  not  to  his  towering 
masonry,  not  to  his  navigable  canal  system,  not  to  his  sky- 
scraping  trestle-work,  nor  to  the  dismal  depths  of  a  hole 


110 

through  a  nil],  bat  with  pride  to  his  perennial  fountain,  to 
his  simple  ditches  and  to  his  broad  expanse  of  fertile  fields, 
where  more  that  is  of  profit  may  be  seen,  as  the  result  of  a 
dollar  spent,  than  can  be  shown  by  any  of  his  neighbors  in 
other  states. 

If  this  true  picture  does  not  soon  attract  the  scrutinizing 
eye  of  capital,  and  Dakota  ere  long  become  their  chosen 
pasture,  then,  indeed,  will  all  signs  fail. 

Water  is  conveyed  from  point  of  supply  to  place  of  distri- 
bution in  ditches,  flumes,  or  pipes,  and  is  distributed  over 
the  land  through  smaller,  lateral-ditches  or  by  plow  fur- 
rows, by  the  actual  flooding  of  the  surface,  or  by  means  of 
sub-irrigation  through  lines  of  tile  pipes;  the  latter  system 
however,  being  confined  almost  exclusively  to  the  irrigation 
of  garden  and  orchard  lands. 

Volumes  might  be  written  on  the  subject  of  water  distri- 
bution and  allied  subjects,  but  the  limit  of  this  little  book 
will  admit  of  but  brief  reference  to  some  of  the  matters 
most  likely  to  engage  the  attention  of  our  farmers. 


3DITOHIES. 
Form  and  Size. 

According  to  a  classification  adopted  by  the  Census  De- 
partment of  Agriculture,  irrigation  ditches  are  divided  into 
three  classes. 

First,  those  under  5  feet  in  width, 

Second,  those  from  5  to  10  feet  wide,  and 

Third,  those  over  10  feet  wide  on  the  bottom,  the  depth 
in  a  general  way  corresponding  with  these  widths  being  1 
foot,  \yz  feet,  and  2^  feet  and  over.  By  reason  of  the  com- 
paratively small  volumes  of  water  to  be  carried,  and  the  re- 
stricted area  to  be  served  from*  any  one  source,  the  Dakota 
irrigation  ditches  will  be  mostly  small;  few,  it  is  safe  to  say, 
need  be  as  large  as  10  feet  in  width.  A  ditch  need  be  only 
large  enough  to  convey  the  water  to  the  place  whence  it  is 
to  be  distributed.  By  "  large  enough  "  is  meant,  of  such  a 
size  as  will  deliver  the  volume  of  water  needed,  at  a  velocity 
not  so  great  as  to  wash  the  banks  of  the  ditch,  and  not  so 
large  as  to  present  a  needless  excess  of  surface  of  bank, 
which  will  increase  the  percentage  of  seepage,  or  of  surface 
to  the  air,  which  will  increase  the  percentage  of  evaporation. 

In  large  ditches  much  depends  upon  the  form  or  sectional 
outline  of  the  excavation  and  banks.  In  smaller  ditches 
this  is  of  less  importance  so  long  as  the  flow  is  not  impeded 
by  the  roughness  of  the  sides  or  by  the  abrupt  changes  of 
direction. 


Ill 

The  same  degree  of  care  in  the  original  construction  and 
future  maintenance  of  ditches  cannot  be  secured  in  a  sec- 
tion where  irrigation  is  first  practiced,  and  where  the  new 
irrigator  has  yet  to  learn  the  importance  of  close  attention 
to  details,  as  in  a  section  where  irrigation  has  long  been 
practiced  and  where  each  detail  of  the  operation  has  been 
reduced  to  a  system. 

The  sooner  attention  is  given  to  the  careful  and  workman- 
like construction  of  ditches,  the  sooner  will  the  labor  devot- 
ed to  irrigation  return  a  satisfactory  profit.  A  channel, 
roughly  scratched  in  the  ground  is  not  a  ditch,  and,  however 
much  the  owner  may  believe  in  its  sufficiency  to  give  proper 
service,  the  flowing  water  cannot  be  deceived  and  will  not 
do  its  full  service  until  given  the  opportunity  which  the 
laws  of  of  hydraulics  have  decreed. 

The  main  distributing  ditches  should  be  built  for  perma- 
nent use.  The  smaller  or  distributing  laterals  may,  in  cer- 
tain cases,  be  cheaply  built  to  serve  the  purpose  for  a  season. 
They  may  be  thrown  out  by  a  double-mould-board  plow  or 
as  a  single  plow  furrow.  The  larger  sections  can  be  most 
cheaply  built  with  ditching  machines.  The  section  of  the 
ditch  may  have  the  form  shown  in  Fig.  17,  where  the  slope 
of  the  bank  in  the  cut  or  excavation  is  one  foot  horizontal 
to  one  foot  vertical.  The  excavated  earth  may,  and  usually 
will,  be  put  into  the  banks  as  shown  at  A,  or  it  may  be 
placed  as  shown  at  B,  where  a  berm,  or  ledge,  b  is  left  at  the 
sides  of  the  ditch.  The  slope  of  the  banks  in  the  embank- 
ment being  1%  to  1. 


Fig.  17 

If  excess  earth  is  required  to  build  the  bank  higher  or  wider 
either  the  ditch  may  be  made  wider  and  deeper  or  the  extra 
eartn  may  be  obtained  from  side  ditches  or  borrow-pits  D, 
or  by  both  means.  It  is  the  province  of  the  engineer  to  di- 
rect as  to  thse  details  of  the  work  so  we  will  here  consider 
only  such  details  as  relate  to  the  ordinary  work  which  the 
farmer  himself  may  be  required  to  perform.  For  all  ordi- 
nary purposes  of  distribution  from  the  reservoirs  to  the 
more  distant  laterals,  main  ditches  from  4  to  6  feet  wide  will 
suffice.  (The  width  of  ditch,  as  stated,  is  understdod  to  be 
the  width  at  the  bottom.) 

The  construction  should  be  workmanlike,  the  bottom  even 
and  free  from  sods,  stones,  lumps,  of  clay,or  weeds;  the  sides 
smooth,  even,  and  free  from  like  obstructions  to  the  even 
and  free  flow  of  the  water. 


112 

Fig.  18    represents 
the  cross  section  of  a 

,  -x  ,  ditch  4  feet  wide  and 

**\      [5*  ^v^  having  water  3  feet 

vSEE  S  deep-  The  area  of 

N«^l  *         Fig.  18  the  wet  section  of  the 

JD      4t        C  ditch  is  equal  to  the 

average    width    multiplied    by  the    depth.     In  this  case 

10ft.  +  4ft_  14 

— 2 —       =  -g-  =7,      7x3=21  sq.  ft.  =  area  of  wet  section 

The  Wet  Perimeter  in  the  length  of  that  portion  of  the 
surface  of  the  cross-section  which  is  covered  by  water,  AB, 
BC,  CD  In  order  to  determine  this  length,  the  length  of 
the  slopes  A  B  and  C  D  must  be  known.  These  may  be 
found,  for  any  depth  of  water  or  for  any  degree  of  slope— as 
follows:  The  slope  is  the  hypothenuse  of  the  right-angled 
triangle  ABE,  and  its  length  is  therefore  equal  to  the 
square  root  of  the  sum  of  the  squares  of  the  other  two  sides. 
In  this  case  the  sides  A  E  and  E  B  are  each  equal  (the  slope 
being  1  to  1)  to  8  feet.  The  sum  of  the  squares  of  A  E  &  E  B 
=9+9=18.  The  square  root  of  18  (see  table  of  roots)=4.2, 
which  is  therefore  the  length  of  A  B.  If  the  slope  had  been 
1J£  to  1,  A  E  would  =  4.5  feet  which  squared=20.25  which 
+9,  the  square  of  E  B,  =  29.25  the  sq.  rt.  of  which=5.4= 
length  of  A  B.  So  with  any  other  depth  or  degree  of  slope. 
In  this  case  the  wet  perimeter  —  4.2+4+4.2=12.4  feet. 

The  "mean  radius" "hydraulic  radius"  "hydraulic  mean 
depth"  and  "mean  depth"  are  synonymous  terms  for  the 

area  of  wet  cross  section         area  A  B  C  D,  Qf  agin 
wet  perimeter  >r  (AB+BC+CD) 

the  above  illustration,      s^t'       =  1.69=mean  radius. 

This  term,  "mean  radius,"  is  frequently  used  in  the  calcu- 
lation of  volumes,  grades,  and  velocities,  by  Kutter's  and 
other  formulae  and  it  is  is  therefore  explained, 

Since  most  slopes  will  be  1  to  1  or  1)^  to  1,  and  most 
depths  from  1  to  5  feet,  and  most  widths  from  2  to  6  feet, 
the  following  table  has  been  prepared  to  show  at  once  the 
lengths  of  the  slopes  A  B  and  C  D  for  slopes  of  1  to  1,  and  of 
1J£  to  1,  and  for  depths  of  1  to  5  feet;  also  the  wet  areas  of 
ditches,  having  bottom  widths  of  2  to  6  feet,  and  water  from 
2  to  2J£  feet  deep;  also  the  lengths  of  the  wet  perimeter,  and 
the  corresponding  mean  radii. 

Application— The  water  in  a  ditch,  having  side  slopes  of  1 
to  1,  is  3%  feet  deep,  what  is  the  length  of  the  wetted  slope 
A  B$  In  second  column,  opposite  depth  of  3J£,  is  4.6= 
length  in  feet  required.  In  third  column  is  5.8= correspond- 
ing length  when  slope=l^  to  1.  A  ditch  has  2}£  feet  of 
water  and  a  bottom  width  of  5  feet,  what  is  area  of  wet  sec- 


1.18 

tion,  length  of  wet  perimeter  and  mean  radius?  Under 
head  of  depth  of  2J£  feet  take  width  of  5  feet;  in  succeeding 
columns  find  A+18.75  sq.  ft,  .  P=\2  ft,  and  R  =  1.56.  The 
limits  of  the  table  will  serve  for  the  ordinary  range  of  work 
and  will  no  doubt  save  some  time  in  making  calculations. 

TABLE  XO.  51. 

TABLE  OF    DEPTHS,  SLOPES,  WET  AREAS,  \VET  PERIMETERS  AND  MEAN 

RADII  OF  SMALL    DITCHES.  X>'>r. 


Slope  of  bank      j 
1  hor.  to  1  vert. 

Slope  of 
bk  14  to  1 

Deptli  of 
water  in 
ditches,  1'1. 

~-~-  -^ 
z  c=~ 

§51 

£>'•= 

Area 
of  wet 
section, 
sq.  feet. 

Length 
of  wet- 
perime- 
ter in  ft 

Mean 
Radius 

Depth  of 
water  in 
feet 

Length 
of  slope 
(ab)  in  ft 

Length  of 
slope  (ab) 
in  feet. 

1 

114 
IH 

134 

2 

m 

SK 

z% 

3 

tit 

34 

s* 

4M 

4u 

434 

5 

1.4 

1.8 
2.1 
2.5 
2'.8 
3.2 
3.5 
3.9 
4.2 
4.6 
4.9 
5.3 
5.7 
6.0 
6.4 
6.7 
7.1 

1.8 
2.2 
2.7 
3.2 
3.6 
4.1 
4.r> 
1.9 
5.4 
:>  N 
6.3 
6.7 
7.2 
7.6 

8.1 
8.5 
9.0 

D. 

w. 

A 

P. 

R 

I 

1 
1 
1 

2 
3 
4 
5 

I: 

6. 

5  .  25 
6  .  75 
S  .  25 
9.75 

'  478 
5.8 
6.8 

7.8 

.625 
.690 
.735 
.76* 

m 

1H 
14 

2 
3 
4 
5 

6.2 

>  •> 
9'.  2 

.847 
.937 
1.01 
1.06 

2 
2 
2 
2 
2 

2 
3 
4 
5 
6 

8. 
10. 
12. 
14. 
16. 

7.6 
8.6 
9.6 
10.6 
11.6 

1.05 
1.16 
1.25 
1.32 
K3§ 

2H 

2l/2 

2V2 
2i/2 

2V»" 

3 
4 
5 
6 

7 

13.75 
16.25 
IS.  75 
21.25 
23.75 

10.              1.37 
11.              1.4S 
12.               1.56 
13.              1.63 
14.               1.70 

Flow  of  Water  in  Ditches. 

This  complex  branch  of  dydraulics  is  treated  exhaustively 
in  several  large  works  on  the  subject,  it  being  of  prime  im- 
portance in  countries  where  water  is  taken  from  rivers,  or 
from  large  storage  basins,  and  carried  for  miles  in  large 
canals  of  ditches.  Important,  because  upon  its  proper  treat- 
ment rests  the  accurate  gauging  of  rivers  and  canals,  or  the 
measurement  of  the  volume  of  water  flowing  in  them.  On 
a  knowledge  of  the  exact  volume  of  the  supply  rests  the 
matter  of  the  volume  of  apportionment  to  different  districts 
or  ditches. 

Many  mechanical  divices  are  used  for  measuring  the  vel- 
ocities of  running  streams,  and  many  formulae  and  rules 
are  given  for  the  calculation  of  the  velocity  and  volume. 

The  Dakota  system  of  irrigation  being  so  entirely  different,  the  necessi- 
ty for  the  accurate  measurement  of  water  in  ditches  is  almost  entirely 
done  away  with ;  so  but  brief  mention  will  be  made  of  a  few  points  in 
this  connection.  The  measurement  of  most  ditches  and  streams  is  in  the 
unit  of  the  cubic  foot  per  second ;  or  the  number  of  cubic  feet  of  water 
the  stream  will  discharge  in  one  second.  The  discharge — for  a  given  depth 
of  water  in  the  ditch— will  depend  upon  the  slope  or  grade  of  the  ditch, 
the  area  of  the  section,  the  condition  of  the  bottom  and  banks,  and  upon 
the  direction  and  force  of  the  wind,  which  exerts  a  considerable  effect 
upon  the  exposed  surface  of  the  water.  [One-tenth  of  the  width  of  sur- 
face being  allowed  for  wind  resistance.] 


114 

As  above  explained,  the  sectional  area  of  any  ditch,  or  of 
the  wet  section  thereof,  is  equal  to  the  average  width  x 
by  the  depth. 

The  velocity  of  a  running  stream  is  not  the  same  at  all 
points  of  the  cross -section,  it  being  least  at  the  bottom  and 
sides,  where  the  friction  is  greatest,  and  less  at  the  surface 
than  at  a  point  a  short  distance  below  it.  The  point  of 
greatest  velocity  is  therefore  at  the  middle  of  the  stream 
and  just  below  the  surface.  To  determine  the  velocity  of 
any  stream  it  becomes  necessary,  therefore,  to  determine 
the  mean  velocity,  or  such  a  velocity  as  would  be  common 
to  all  the  threads  of  water  of  the  stream  if  the  discharge  re- 
mained the  same  and  all  flowed  at  the  same  rate. 

Current  meters  and  other  mechanical  devices  are  used  to 
determine  the  velocity  of  the  current  at  several  points  in 
the  cross-section,  and  from  a  reduction  of  these  observa- 
tions a  mean  is  obtained  for  the  whole  section. 

Intricate  formulae  are  likewise  employed  to  determine 
the  velocity  and  discharge,  mathematically;  but  their  ap- 
plication, involving  a  considerable  knowledge  of  mathema- 
tics and  hydraulics,  they  are  not  popular  with  the  average 
irrigator.  The  simplest  way  to  determine  the  approximate 
mean  velocity  of  a  stream  is  to  take  a  certain  percentage 
of  the  ascertained  maximim  surface  velocity.  By  experi- 
ment the  mean  velocity  has  been  found  to  be  from  80  to  85 
per  cent  of  the  maximum  Mirface  velocity.  In  this  country 
80  per  cent  is  usually  taken  as  the  standard.  To  determine 
the  maximum  surface  velocity,  select  a  straight  section  of 
ditch,  in  good  repair,  and  stake  out  a  section  of  100  feet. 
Place  in  the  current — at  a  short  distance  above  the  upper 
stake— a  small  block  of  wood,  so  that  when  it  passes  the 
upper  stake  it  will  have  acquired  the  velocity  of  the  water. 
]N  ote  carefully  the  exact  time  of  its  passage  of  both  the  up- 
per and  the  lower  stakes,  and  record  the  interval.  Repeat 
this,  say  four  or  five  times,  and  take  an  average  of  the  in- 
tervals to  get  the  nearest  true  interval. 

Example,— 1st.  interval  =  25  seconds. 

2d.        "  24 

3d.        "  25 

4th.      "  26        " 

100  which  H-  4  —  25  sec.  =  aver- 
age interval.  If  the  current  runs  100  feet  in  25  seconds  it 
runs  J^  =  4  feet  per  second,  —  maximun  surface  velocity. 
80  per  cent  of  4  feet  =  3.2  feet  per  second  —  the  mean 
velocity  of  the  stream. 

The  volume  in  cubic  feet  discharged  will  of  course  equal 
the  wet  area  X  by  the  mean  velocity.  Assume  the  ditch  to 
be  5  feet  wide  and  the  water  2  feet  deep.  From  table  No.  51 
we  find  the  wet  section  to  have  an  area  of  14  square  feet. 
Then  14  x  3.2  (area  X  mean  vel.)  =  44.8  =  cubic  feet  per 
second  discharged.  Table  36  shows  this  to  be  equal  to  335 


115 

gallons  per  second.  The  section  of  ditch  should  be  in  good 
condition  and  fairly  uniform  in  section. 

The  determination  of  the  velocity  and  volume,  as  above 
described,  necessitates  the  measurement  of  the  surface  velo- 
city. Where  formulae  are  used  this  is  not  necessary. 

As  above  stated,  the  use  of  formulae  not  being  convenient 
to  the  average  irrigator,  and  the  space  within  the  limit  of 
this  little  book  being  insufficient  to  properly  explain  even 
the  simpler  ones,  the  subject  will  not  be  considered.  The 
reader  being  referred  to  such  standard  works  as  Trautwine's 
Engineer's  Pocket  Book— where  the  formula  of  Kutter  is 
fully  explained  and  illustrated  by  examples  and  tables  of 
coefficients  (P.  571  to  2796,  in  editions  of  1888  or  1891);  Wies- 
bach's  Mechanics,  where  is  found  a  much  simpler  formula, 
and  one  more  convenient,  with  table  of  coefficients;  and  to 
the  recent  exhaustive  work  of  P.  J.  Flynn  on  Irrigation,  and 
the  Flow  of  Water  in  Open  Canals.  (See  advertisement  of 
Irrigation  Age);  as  well  as  to  any  of  the  many  standard 
works  on  hydraulics. 

Grades. 

A  study  of  the  details  of  the  larger  canals  or  ditches  of 
the  west  shows  a  great  variety  of  sizes  and  grades,  yet  more 
uniformity  than  some  would  expect.  Ditches  running  from 
20  to  over  100  miles  have  widths  from  20  to  80  feet,  some  be- 
ing built  with,  and  some  without,  berms;  the  grades  ranging 
from  1  foot  to  7  feet  per  mile.  The  steeper  grades  are  not 
common  and  are  for  short  distances  only.  The  average 
grades  for  main  ditches,  carrying  from  2  to  6  feet  of  water, 
are  from  1J^  to  2%  feet  per  mile.  Such  low  grades  will  an- 
swer only  for  the  larger  ditches  carrying  large  volumes  of 
water  and  where  the  ratio  of  volume  to  resistance,  or  friction 
on  the  sides,  is  large. 

In  smaller  distributing  ditches,  where  the  volume  is  small- 
er, and  the  resistance  proportionately  much  greater,  a  steep- 
er grade  must  be  allowed.  It  is  frequently  said  by  those  who 
are  not  informed  that  this  country  is  too  level  to  irrigate  to 
advantage. 

Such  is  far  from  being  the  case.  The  writter  has  yet  to 
find  a  quarter  section  of  land,  in  the  most  level  portion  of 
the  James  river  valley,  that  is  too  level  to  irrigate.  The 
gently  rolling  lands,  or  such  as  have  a  comparatively  uni- 
form slope,  are  the  best  located  for  irrigation. 

The  location  of  the  well  or  reservoir,  on  or  near  the  high- 
est point,  fixes  the  point  of  radiation  of  the  ditches,  their 
lines  being  located  according  to  the  grades  secured  and  the 
lay  of  the  land  to  be  served.  The  aim  will  always  be  to 
keep  the  water  up  as  high  as  possible  for  it  is  useless  to  sac- 
rifice grade  or  make  a  ditch  run  at  a  greater  grade  than  is 
necessary.  It  is  an  easy  matter  to  let  the  water  down  but  a 
difficult  thing  to  raise  it.  By  keeping  the  grades  up,  a  broad- 
er area  is  kept  within  the  range  of  service. 


116 

Grades  of  from  2  to  5  feet  per  mile  will  be  ample  to  secure 
good  delivery  from  the  smaller  main  ditches,  while  the  later- 
als will  require  steeper  grades,  which,  in  many  cases,  may 
be  confined  to  the  approximate  level  of  the  field,  except  on 
hill  sides  or  quite  abrupt  slopes,  in  which  case  the  grades 
will  be  carried  around  the  slope  as  contours.  The  following 
table  will  show  the  grades  per  100  feet  corresponding  to  giv- 
en grades  per  mile.  If  the  grade  per  rod  is  required  it  may 
be  taken  approximately  from  the  table  by  taking  |  of  the 
grade  for  100  feet.  If  the  grade  is  required  exactly  for  any 
given  distance,  and  corresponding  to  any  given  grade  per 
mile,  it  may  be  found  by  simple  proportion,  thus: 
grade  per  mile  :  one  mile  :  :  required  grade  :  given  distance. 

Example,— What  is  the  grade  for  3,500  feet,  corresponding 
to  a  grade  of  10  feet  per  mile  ? 

10  : 5280  ::(?):  3500  =  35000  4-  5280  =  6.62  =  Ans. 
or  10  :  5280  :  :  6.62  :  3500. 

That  is,  the  given  distance  multiplied  by  the  grade  per 
mile  and  the  product  divided  by  5280,  the  number  of  feet  in 
a  mile,  equals  the  required  grade.  In  this  way  any  grades, 
other  than  those  given  in  the  table,  may  be  found.  In  like 
manner  the  grade  per  mile,  corresponding  to  the  grade  for 
any  given  distance,  would  be  found,  thus: 

grade  per  mile  ( ?)  :  5280  :  :  given  grade  :  given  distance. 

TABLE  NO.  52. 

Table  of  Grades  per  Mile;  or  per  100  ft.  measured  horizontally . 

From  Trautwine. 


Grade 
in  ft. 

Grade  in  feet 
per  100  feet. 

NOTE. 

Grade 
in  ft. 

Grade  per  100 
feet. 

per  mi. 

per  mi. 

1 

.01894 

If  the  grade  per  mile  con- 

.05 

.00094 

2 

.03788 

sists  of  feet  and  tenths  add 

.1 

.00189 

3 

.05682 

to  the  grade  per  100  ft.  as 

.15 

.00283 

4 

.07576 

given  in  the  first    table  , 

2 

.00379 

5 

.09470 

the  grade  per  loo  feet  for 

>25 

.00473 

6 

.11364 

the    required  tenths,    as 

.3 

.00568 

7 

.  13258 

given  in  the  second  table. 

.35 

.00662 

8 

.15152 

Example,  Grade  per  mile 

.4 

.00758 

9 

.  17045 

—  12.85   ft*  what  is  grade 

.45 

.00852 

10 

.  18939 

per  100  feet  and  in  725 

.5 

.00947 

11 

.20833 

ft.?    .22727  +  .01609  = 

.55 

.01041 

12 

.22727 

.24336  =    grade   in    loo 

.6 

.01136 

13 

.24621 

ft.  .24336  X  7  =  i-7°352 

.65 

.01230 

14 

.26515 

=  grade   in    700   ft.    and 

.7 

.01326 

15 

.28409 

.24336  -*-  4  =   .06084  = 

.75 

.01420 

16 

.303  '3 

grade  in  25  ft.        1.70352 

.8 

.01515 

17 

.32197 

+  .06084  "=    1.76436    = 

.85 

.01609 

18 

.34091 

grade  for  725  feet.      OR 

.9 

.01705 

19 

.35985 

•24336  x  7-25  =  1.76436 

.95 

.01799 

20 

.37879 

1.0 

.01894 

117 
Laying  Out. 

The  laying  out  of  the  ditches  is  the  provience  of  the  en- 
gineer or  surveyor,  although  the  more  intelligent  farmers 
may  do  much  of  their  own  work  and  thus  save  considerable 
expense.  In  the  arrangement  of  fields  it  may  become  nec- 
essary to  change  the  location  of  a  ditch  or  to  lay  out  a  new 
one.  This  work  the  farmer  may  do  with  simple  means,  al- 
though, in  many  cases,  it  will  pay  an  intelligent  farmer  to 
own  a  drainage  "level.  Its  use  on'his  own,  and  on  his  neigh- 
bors' work,  will  soon  pay  for  it.  Simple  devices  for  small 
jobs  will  be  described  later  on. 

Something  of  a  knowledge  of  leveling  must  be  had  in  order 
to  do  the  work,  but  sufficient  may  soon  be  acquired  to  per- 
mit of  much  home-work  being  done.  If  any  doubt  exists  as 
to  ones  ability  to  lay  out  a  piece  of  work  it  will  be  cheaper 
to  hire  some  one  to  do  it  who  knows  how. 

The  running  of  preliminary  lines,  making  of  profiles,  cross 
sectioning,  calculation  of  sizes,  carrying  capacities,  and 
grades,  and  the  final  location  and  construction  are  details 
of  the  work,  each  the  proper  subject  of  a  chapter.  The  limit 
of  this  little  book  will  not  permit,  however,  of  any  special 
consideration  of  these  purely  technical  details  of  the  work . 
(See  remarks  on  leveling,  P.  132  to  134.) 


Excavation  and  Cost. 

The  smaller  ditches  may  be  constructed  by  hand-shovel- 
ing, by  plowing  and  scraping,  or  by  plowing  with  a  large 
double-mould-board  plow.  The  larger  ditches  by  plowing 
and  scraping,  or  by  grading  or  ditching  machines.  Hand 
work  is  of  course  most  expensive  but  it  will  be  necessary  in 
some  places.  Simple  piowed  ditches  are  of  course  the  cheap- 
est, as  they  are  also  but  temporary,  and  in  the  end  the  more 
expensive.  Scraper  woak  will  cover  the  greatest  range  of 
work  and  will  fairly  represent  the  average  cost.  Work  done 
with  a  ditching  machine  is  very  satisfactory  and  far  cheaper 
than  other  work. 

The  New  Era  grader  and  ditcher  (see  advertisement)  is 
the  leading  machine  of  its  class.  It  will  place  in  the  bank 
from  1000  to  1400  cubic  yards  of  earth  per  day  at  a  cost  of 
about  2  cents  per  yard;  or  it  will  load  from  600  to  800  wagons 
per  day.  It  has  been  used  in  all  states,  in  all  soils,  and  on 
all  classes  of  work  with  full  satisfaction  and  great  economy. 
Its  use  on  reservoirs  is  especially  recommended.  Done  with 
a  ditcher,  the  ditches  on  a  section  of  average  land  need  not 
cost  to  exceed  $200,  or  $50  per  quarter  section.  Under  fav- 
orable circumstances  the  work  has  been  done  for  half  this 
sum.  (See  also  page  246.) 

Dakota's  soil  and  topography  renders  the  operation  of  a 
grader  easy,  economical  and  altogether  satisfactory. 


118 

No  farmer  can  afford  to  buy  a  machine  to  do  his  own  work 
alone,  but  when  farmers  become  associated  in  the  putting 
down  of  wells  and  construction  of  reservoirs  and  ditches, 
then  it  will  pay  to  buy  machines,  for  on  a  large  job  they  will 
soon  save  their  cost.  The  suggestion  is  made  that  town- 
ships or  counties  purchase  not  only  drilling  outfits  but  also 
ditching  outfits.  Each  farmer  could  pay  for  its  use  on  his 
work,  at  such  a  rate  as  would  effect  a  great  saving  to  him- 
self, and,  at  the  same  time,  soon  return  to  the  township  the 
cost  of  the  machine.  An  additional  advantage  of  such  an 
arrangement  would  be  in  the  use  of  the  grader  on  the  pub- 
lic roads  where  much  cost  to  the  tax-payers  could  be  saved 
thereby. 

In  this,  as  in  all  other  fields,  the  machine  has  come  to 
stay  as  against  all  other  forms  of  labor. 

The  suggestion  here  made  will  bear  careful  consideration 
by  associations  of  farmers  or  by  townships  and  counties. 

Most  of  the  railway  grading-  in  the  state  has  been  sub-let 
to  f arme  s  and  others  at  from  6  to  8  cents  per  yard,  at  wrhich 
rate— and  on  large  contracts,  there  is  only  fair  wages. 

Table  No.  49  shows  the  cost  of  grading  reservoir  embank- 
ments at  the  rate  of  6  and  8  cents  per  yard .  A  reservoir  of 
5  acres,  having  an  8  foot  bank,  would  cost  $746  at  8  cents 
per  yard.  Four  such  reservoirs  on  adjacent  farms  would 
cost  about  $3,000.  If  done  with  a  grading  machine,  at  a 
cost  of  even  3  cents  per  yard,  there  would,  on  that  small  job, 
be  a  clear  saying  of  $1,500  over  other  work  Such  conserva- 
tive illustrations  show  the  value  of  properly  considering  the 
means  of  doing  the  work.  What  applies  to  reservoirs  ap- 
plies likewise  to  ditches. 

Embankments  and  Footings. 

Under  the  head  "  Reservoirs, "  on  page  99,  the  qualified 
statement  is  made  that  the  use  of  drag-scrapers  will  result 
in  a  more  solid  bank  than  when  scrapers  or  graders  are  used. 
This  is  commonly  so;  but  not  necessarily  so,  for  if  the  grad- 
er-work is  properly  followed  up  with  a  harrow  the  earth  is 
torn,  mixed,  and  more  thoroughly  compacted  than  in  any 
other  way  and  the  resulting  embankment  is  as  good  as  if 
done  by  any  other  means. 

The  object  in  any  embankment  is  to  have  it  sufficiently 
solid  to  hold  water.  Around  gates  and  outlets  the  earth 
should  be  solidly  tamped  or  puddled— wetted  down— in 
order  to  make  a  tight  joint.  So,  too,  with  the  footings  of 
high  banks,  they  require  special  attention.  If  the  dirt  is 
thrown  loosely  on  top  ef  the  sod  the  water  may  percolate 
through  the  loose,  filter-like  footing  of  grass  and  weeds  and 
cause  a  leak,  and  possibly  a  wash-out  of  the  Dank. 

To  insure  against  this  there  should  be,  along  the  middle- 
line  of  every  heavy  bank,  several  plow  furrows  turned  and 
the  sod  cast  aside*  The  fresh  earth  of  the  bank  settles  into 


119 

the  trench  and  soon  forms  a  tight  joint  with  the  solid  sur- 
face. If  the  banks  are  but  6  or  8  feet  high,  this  will  suffice ; 
but  if  they  are  higher  the  trench  may  better  be  double- 
plowed  and  a  bank  of  wet  earth  piled  in  and  over  it  thus 
insuring  a  compact  core  for  the  bank . 

Reference  has  been  made  to  the  slope  of  the  banks.  The 
slope  in  the  excavation  need  not  usually  be  more  that  1  to  1, 
but  if  the  cut  is  of  any  considerable  depth,  and  the  soil 
sandy  or  loose,  then  a  slope  of  1%  to  1  will  be  better. 

The  slope  in  the  fill  or  banks  may  usually  be  1%  to  1,  but 
if  they  are  high  a  slope  of  2  to  1,  on  the  wet  side,  will  be 
safer.  The  slopes  of  the  reservoir  banks  are  thus  given  in 
the  diagrams  and  tables  under  head  of  reservoirs. 

Cubic  Contents  of  Excavations. 

Tables  giving  the  cubic  contents,  per  unit  of  length,  for 
ditches  of  different  depths,  widths,  and  slopes,  would  be  con- 
venient for  reference,  but  they  would  necessarily  be  long  in 
order  to  cover  the  whole  ground.  On  this  account  they  will 
be  omitted  and  the  simple  rule  given  by  which  the  calcina- 
tions may  be  made  in  any  given  case. 

RULE:  Multiply  the  area  of  the  section  of  the  ditch,  in 
square  feet,  by  the  length  of  the  ditch,  in  feet,  and  divide 
the  product  by  27  to  get  the  cubic  yards  of  earth  in  the 
ditch. 

Determine  the  area  of  the  section  as  explained  in  connec- 
tion with  table  51. 

Example— How  many  cubic  yards  in  a  ditch  4  feet  wide, 
2)4  feet  deep,  and  1835  feet  long  V .  Bottom  width  4  feet+top 
width  8^  feet  — 12}^  which H- 2 =Q%= average  width.  6^ 
X2J^,  the  depth, =14.0625= area,  and  cubic  yards  in  I  ft.  of 
ditch.  14.0625x1835,  the  length,=25,805  cu.  ft.  which-^27=: 
956= cubic  yards. 

To  get  the  contents  of  the  ditch  in  gallons,  proceed  as 
above,  using  the  wet  section— and  multiply  the  volume  in 
cubic  feet  by  7.48052  to  get  volume  in  gallons. 

Gates.  The  gates  or  outlets  from  the  main  ditches  to 
the  laterals  are  too  simple  in  construction  to  need  illustra- 
tion or  special  consideration.  They  may  be  made  with 
more  or  less  complication,  but  a  simple  frame  of  plank  with 
a  board  or  plank  slide  or  gate,  fitted  to  slide  vertically 
within  cleats  will  answer  every  purpose.  When  the  gate  is 
down— closed— the  mud  in  the  ditch  may  be  drawn  about  the 
base  and  sides  to  aid  in  keeping  it  water  tight. 

In  the  working  laterals,  where  it  is  desired  either  to  cut 
off  any  further  flow  or  to  dam  up  the  water  for  the  flooding 
of  a  certain  area,  a  small  portable  dam  or  stop  of  sheet  iron 
or  wood  may  be  used.  In  case  the  water  passing  from  the 
main  ditch  to  the  laterals  is  to  be  measured  or  gauged  then 
the  common  gate  will  give  place  to  the  weir  or  to  the  spill- 
box  shown  in  Fig.  6. 


120 

•  One  matter  will  be  mentioned  as  to  the  location  of  ditches 
— the  same  applying  to  both  flumes  and  pipe-lines— which 
is  to  locate  them,  as  nearly  as  circumstances  of  economy, 
grades,  &c  will  permit,  on  such  courses  as  will  permit  of  the 
proper  working  of  the  land.  Rectangular  areas  are  the 
most  convenient  to  cultivate,  and  sharp  angular  pieces  the 
most  difficult.  So,  in  locating  water-ways  some  considera- 
tion should  be  given  to  the  after  convenience  of  handling 
machinery  in  the  cultivation  of  the  land.  A  moderate  in- 
crease of  the  first  cost  of  the  water-way  would  be  justified 
in  an  effort  to  secure  an  area  more  favorable  in  form  to 
convenient  cultivation  or  access  from  other  parts  of  the 
land. 

Flumes. 

Flumes  are  boxes  or  troughs  used  to  convey  water  where 
ditches  are  impracticable  or  needlessly  expensive  either  to 
construct  or  to  maintain.  Where  a  ravine,  valley,  or  any 
considerable  depression  crosses  the  line  of  a  ditch  the  water 
may  be  turned  into  a  flume,  carried  over  the  depression,  and 
then  discharged  into  another  ditch  on  the  farther  side.  It 
may,  too,  be  advisable  to  carry  the  water  in  a  flume  over 
loose,  sandy  soil,  where  the  loss  by  percolation  would  be  so 
excessive  as  to  render  a  sufficient  delivery  from  an  open 
ditch  either  difficult  or  impossible. 

Many  cases  will  therefore  arise  where  the  use  of  flumes 
will  either  save  the  farmer  considerable  expense  or  conserve 
his  greater  convenience.  Special  forms  of  sheet  iron,  or 
other  sheet  metal,  flumes  are  much  used  in  mountainous 
sections  because  of  their  lightness,  tightness,  and  economy, 
and  the  facility  of  erecting  them  in  difficult  places. 

As  usually  constructed  flumes  are  merely  wooden  boxes, 
open  at  the  top,  and  of  such  size  and  strength  as  is  neces- 
sary to  carry  and  support  the  water  supplied.  Many  in  the 
west  are  of  large  size,  great  strength,  and  traverse  long 
distances  and  at  great  height.  Such  as  Dakota  farmers  will 
use  will  be  small,  short  and  low.  The  grades  may,  if  neces- 
sary, be  somewhat  lighter,  and  the  size  smaller,  than  those 
of  the  ditches  supplying  them,  because  of  the  lesser  friction 
and  the  greater  facility  of  flow.  The  volume  of  water  to  be 
carried  will  regulate  the  size  the  same  as  in  ditches  and  the 

§rade  will,  in  the  same  way,  regulate  the  carrying  capacity 
y  increasing  or  decreasing  the  velocity  of  the  current. 

The  effect  of  friction  of  the  water  upon  the  sides  of  the 
flume,  and  of  even  a  gentle  wind  upon  the  surface  of  the 
water,  will  be  quite  noticeable— more  so  than  in  a  ditch. 
An  instance  is  cited.  A  flume  12  x  18  inches  by  800  feet 
long,  with  a  fall  of  2  feet,  ran  to  overflowing  at  the  upper 
end  while  discharging  but  3  inches  at  the  lower  end.  Wind 
and  friction  prevented  the  water  from  running. 


121 

Since  the  delivery  depends  upon  the  vel  ocity  of  flow,  and 
since  the  velocity  in  an  open  water-way  is  due  solely  to 
gravity,  and  not  to  any  confined  head  or  pressure,  the  deliv- 
ering capacity  of  a  flume  will  be  governed  by  the  size  and 
grade  not  by  the  size  of  a  pipe  delivering  water  to  it  under 
high  pressure.  The  volume  and  relative  velocities  must  be 
considered.  If  the  volume  to  be  carried  is  that  of  the  well 
alone,  as  where  the  flume  is  used  to  carry  the  water  from 
the  well  to  the  ditches  or  the  reservoir,  the  size  may  be  mod- 
erate as  compared  with  that  of  a  flume  farther  away  and- 
forming  part  of  the  waterway  from  a  reservoir  from  which  a 
much  larger  volume  will  flow  at  one  time  than  would  flow 
from  the  well  alone. 

The  flume  box  may  be  made  of  2  inch  plank,  selected  as 
free  from  loose  knots  or  cracks,  closely  spiked  with  5  or  6 
penny  wire  spikes  (wire  spikes  will  hold  better  than  others 
and  are  less  apt  to  split  the  wood  in  driving.) 

If  a  small  box  is  needed  a  single  plank  of  14  to  18  in.  will  do 
for  the  bottom,  and  similar  ones  for  the  sides.  The  addition 
of  a  second  plank  to  the  bottom,  the  sides  remaining  the 
same,  will  double  the  volume  and  a  little  more  than  double 
the  carrying  capacity  of  the  flume,and  at  but  slight  increase 
of  expense  for  the  supports,  braces,  etc.,  may  remain  sub- 
stantially the  same.  The  construction  of  a  flume  is  but  a 
simple  matter.  Any  carpenter  or  intelligent  farmer  can 
'  build  one. 

The  supports  may  in  many  cases  be  a  single  line  of  heavy 
fence  posts,  which  may  be  had  in  lengths  as  great  as  12  or 
14  feet.  The  buts  set  2  or  3  feet  in  the  ground,  and  well 
tamped,  give  a  good  foundation.  The  grade  line  for  the 
tops  is  marked  by  leveling,  and  the  tops  then  sawed  to 
grade,  the  caps  or  cross  bars  spiked  to  the  posts,  and  the 
flume  then  constructed  on  these.  If  of  6  feet  or  more  in 
height  the  posts  and  cross  bars  had  better  be  braced  to  pre- 
vent the  rocking  of  the  flume  by  heavy  winds. 

Where  greater  heights  than  10  or  12  feet  are  met  a  trestle 
of  timber  posts,  properly  footed,  braced,  and  anchored,  will 
be  used.  The  rigidity  of  the  supporting  posts  should  be 
carefully  looked  to  in  this  country  of  almost  constant  and 
heavy  winds,  for  upon  this  will  depend  very  largely  the 
tightness  of  the  flume  and  its  freedom  from  leakage. 

The  planks,  before  being  spiked  together,  should  be  paint- 
ed along  the  edges  in  contact,  with  a  coat  of  very  thick 
paint.  This  will  not  only  aid  in  making  a  water  tight  joint 
but  will  preserve  the  wood  at  the  joint.  The  edges  of  the 
planks  should  be  dressed  true  so  as  to  fit  properly.  As 
rough  sawed  by  the  mill  they  are  often  wavy  or  uneven. 
Cut  out  all  warped  or  crooked  pieces  for  they  cannot  be 
worked  in  to  advantage. 

If  double  widths  of  plank  are  used  on  the  bottom  or  sides 
they  should  be  tongued  and  grooved  if  possible,  or  at  least 


122 

carefully  matched  and  secured  in  close  contact  by  cross 
pieces.  The  joints  of  the  plank  at  the  "bents"  or  supports, 
will  be  protected  by  side  strips  or  braces  and  the  box,  at  in- 
tervals between  the  bents,  will  be  surrounded  by  strips  or 
wooden  braces  to  give  rigidity  to  the  flume  and  prevent 
loosening  of  the  joints. 

The  length  of  the  space  between  the  bents  will  depend 
somewhat  on  the  style  of  the  flume  or  upon  the  length  of 
the  lumber  used.  Where  a  single  line  of  posts  is  used  have 
the  bents  at  the  ends  and  middle  of  each  length  of  16  or  18  ft. 
plank  (8  or  9  foot  spaces.)  If  the  flume  is  more  solidly  built 
20  foot  lumber  may  as  well  be  used,  leaving  10  foot  spaces. 
If  the  ditch  is  large,  and  the  flume  correspondingly  large, 
the  trestles  must  be  heavier  and  a  line  of  stringers  will  sup- 
port the  flume  between  the  bents. 

The  dressed  surface  of  the  lumber  will  be  on  the  inside  of 
the  box  to  present  as  smooth  a  surface  as  possible  to  the 
running  water.  After  the  completion  of  the  flume  go  over 
all  the  joints  with  a  coat  of  thick  paint  applied  with  an  old 
stiff  brush.  By  so  doing,  and  using  care  and  plenty  of  nails, 
a  box  may  be  made  that  is  perfectly  watei  tight.  A  small 
leak  may  often  be  stopped  by  filling  the  crack  with  stilt' clay 
or  mud.  The  details  of  construction  will  depend  somewhat 
upon  the  builder  and  his  means,  but  they  are  so  simple  as  to 
render  further  suggestion  unnecessary. 

PIPES.  The  use  of  pipe-lines  for  conveying  water,  in  the 
place  of  ditches  or  flumes,  has  increased  much  since  the  in- 
troduction of  certain  cheaper  forms  of  pipe.  In  the  west, 
pipes  of  wood,  banded  with  iron,  are  extensively  used  as  are 
pipes  of  spiral-riveted  or  welded  iron  or  steel.  These  latter 
combining  great  strength  with  lightness  and  economy. 

Where  waters  can  be  forced  under  heavy  pressure,  as  from 
our  wells,  the  use  of  surface  pipe-lines  of  light  pipe  will  find 
a  broad  field  of  usefulness  and  should  receive  such  consider- 
tion  as  its  merits  deserve;  especially  where  the  work  of  con- 
structing ditches  or  flumes  is  of  any  special  magnitude. 
The  pipe-line  is  intended  to  take  the  place  of  the  main  ditch 
or  flume  and  not  of  the  distributing  laterals.  The  advant- 
age of  a  pipe-line  over  a  ditch  lies  in  this— that  the  water 
supply  is  not  reduced  by  seepage  or  evaporation  and  the 
duty  of  the  well  is  thereby  increased.  The  area  of  surface 
occupied  by  the  pipe  line  is  not  nearly  so  great  as  the  area 
occupied  by  the  ditch  and  embankments  and  thus  the  area 
subject  to  cultivation  in  increased.  The  cost  of  mainte- 
nance is  less,  for  a  pipe-line  will  need  but  little  attention, 
whereas,  ditches,  however  well  they  may  be  made, 
will  require  .an  annual  overhauling;  especially  if  made  of 
loose  or  sandy  soil  which  in  a  windy  country  soon  blows 


123 

down.  The  matter  of  grade  is  of  no  importance  for  the  wa- 
ter, being  forced,  will  run  up  hill  as  well  as  down  and  the 
pipe  may  be  laid  to  the  grade  of  the  surface  and  deliver 
water  at  a  level  higher  than  the  well.  The  area  under  ser- 
vice from  the  well  may  thereby  be  increased  by  rendering  it 
possible  to  reach  areas  to  which  gravity  alone  would  not 
carry  the  water.  In  this  way  a  well  owner  may  be  enabled 
to  sell  and  deliver  water  to  a  neighbor  whose  land  lies,  or 
is  controlled  from  a  higher  level.  The  advantage  over  a 
flume  lies  in  the  fact  that  evaporation  and  leakage  are  done- 
away  with.  The  delivering  capacity  is  greater  because  un- 
der pressure.  The  first  cost  may  be  less  even  than  that  of 
the  flumes,  and  the  cost  of  maintenance  less.  The  matter 
of  grade  is  eliminated  and  the  line  is  on  or  near  the  surface 
where  it  may  be  more  easily  constructed  or  repaired  and 
where  less  liable  to  damage  from  winds.  The  alignment,  or 
location,  too,  may  be  accommodated  to  the  circumstances  of 
the  surroundings  more  readily  than  that  of  either  ditches  or 
flumes. 


It  is  here  assumed  that  the  pipe  line  connects  with  the 
well;  otherwise  there  could  be  no  pressure  upon  the  pipe 
and  it  would  stand,  in  relation  to  delivery,  on  a  plane  with 
the  ditch  or  flume. 

If  the  line  is  accommodated  to  the  surface  and  there  is  any 
inverted  or  downward  bend  in  the  pipe  there  should  be  a 
valve  set  at  the  lowest  point  to  permit  of  emptying  or  drain- 
ing the  pipe  during  the  cold  weather  or  for  repairs.  The 
pipe  may  be  laid  on  or  near  the  surface  on  low  supports  of 
such  form  and  material  as  circumstances  may  suggest.  It 
should,  at  suitable  intervals,  be  fastened  or  anchored  down 
in  some  suitable  way  to  prevent  displacement  by  the  wind 
or  by  other  means,  and  it  should  be  painted  to  preserve  it 
from  rust. 

The  concluding  remark  as  to  location  of  ditches  may  be 
again  referred  to  in  this  connection,  and  the  suggestion 
made  that  the  location  of  the  lines  of  the  water-ways  be 
made  as  far  as  possible  along  the  lines  of  the  fields  or  along 
fences  or  roads.  In  the  case  of  the  smaller  pipe-lines  the 
fences  themselves  will  often  serve  as  sufficient  and  conven- 
ient supports  for  the  pipe,  intermediate  supports  being  set 
if  necessary.  In  view  of  the  advantages  possessed,  under 
certain  conditions,  by  pipe-lines  over  other  forms  of  water- 
ways one  should  fully  consider  the  advantages  of  each  as 
well  as  the  cost  and  maintenance  before  deciding  which  to 
adopt.  On  most  lands  there  will  be  no  use  for  either  pipe- 
lines or  flumes.  Their  service  is  justified  only  by  the  circum- 
stances of  the  topography  and  service. 


124 
HYDRAULIC  RAM. 

The  occasion  will  frequently  arise  where  the  area  to  be 
irrigated  is  divided  by  a  water  course,  gully,  or  other  depres- 
sion, the  land  on  the  side  of  the  well  and  reservoir  sloping 
gently  toward  the  "  draw, "  the  opposite  side  of  which  is  high 
and  comparatively  level.  The  well  and  reservoir  being  at  a 
distance  from  the  draw  it  will  hardly  pay  to  lay  a  pipe  line 
to  serve  the  other  side  and  the  water  cannot  be  carried 
across  by  ditch  or  flume.  How  then  can  it  be  delivered  into 
a  ditch  on  the  opposite  and  higher  ground?  By  elevating  it 
only.  This  could  be  done  from  the  end  of  an  open  ditch  on 
the  low  side  by  means  of  a  steam  or  wind  pump.  The  for- 
mer way,  by  reason  of  fuel  and  attendance,  would  not  prove 
profitable,  and  the  latter  way  possibly  ineffectual  in  spite  of 
an  abundant  supply.  A  simple  and  inexpensive  water 
elevator  may  be  had  in  the  hydraulic  engine  or  ram  which 
may  be  so  set  as  to  take  the  supply  from  the  open  ditch, 
with  a  fall  of  such  an  amount  as  the  slope  will  permit,  leav- 
ing drainage  away  from  the  ram. 

By  this  means  the  water  may  be  forced  across  the  draw  in 
a  constant  stream,  working  night  and  day,  rain  or  shine,  and 
without  fuel,  attention,  cost,  or  care. 

*  The  Rife's  Hydraulic  Engine  (See  advertisement,  P.  214)  is 
such  a  machine  and  one  of  high  efficiency.  The  No.  40  ma- 
chine is  fitted  with  a  4-inch  supply  pipe  and  a  2-inch  dis- 
charge pipe,  and,  with  a  fall  of  from  4  to  6  feet,  it  will  raise 
from  60  to  70  gallons  per  minute  to  a  height  of  20  feet  or 
more,  and  lesser  volumes  to  much  greater  heights.  The 
machine  will  work  under  heads  of  but  one  or  two  feet  and 
in  such  cases  it  could  often  be  used  to  advantage  along  side 
slopes  to  raise  a  supply  of  water  to  a  ditch  at  a  higher  level. 

Such  appliances,    together  with  wind  mills  and  steam 

Simps,  will,  in  the  near  future,  find  a  welcome  place  among 
akota  irrigators,  for,  although  a  well  will  do  almost  any- 
thing within  its  immediate  reach,  there  will  be  duties  to 
perform  in  connection  with  a  properly  managed  irrigation 
system  which  are  outside  of  the  sphere  of  the  well  itself,  yet 
properly  within  the  sphere  of  other  appliances,  all  of  which 
must  be  considered  if  the  greatest  good  is  desired  and 
secured. 

PUMPS. 

While  this  little  book  is  devoted  most  especially  to  a  con- 
sideration of  artesian  wells  as  a  source  of  water  supply  for 
irrigation,  it  must  not  be  forgotten  that  there  are  other 
sources  of  supply.  Dakota  has  few  lakes  or  rivers  from 
which  any  supply  could  be  drawn,  except  of  course  the 
Missouri,  the  supply  from  which  is  practically  inexhaust  ible. 

There  are  many  sections  all  over  the  states  where  large, 
shallow  wells  may  be  sunk  into  the  sand  and  gravel  beds 


125 

from  which  an  almost  inexhaustible  water  supply  may  be 
obtained.  It  must  of  course  be  elevated  by  artificial  means 
and  the  question  will  at  once  suggest  itself  as  to  whether  it 
will  pay  to  do  this. 

Yes,  It  Will  Pay! 

As  to  this  there  can  be  no  question,  and  ere  long  this 
source  of  water  supply  will  cut  a  very  large  figure  in  the  ir- 
rigation of  lands  in  Dakota. 

Certain  very  erroneous  and  misleading  statements  have 
been  made  by  government  specialists  and  agents  as  to  the 
relative  value  of  these  phreatic  or  sub-surface  waters,  and 
the  true  artesian  waters;  they  claiming  that  by  far  the  larger 
supply  was  the  sub-surface  supply.  These  statements  and 
reports  were  founded  upon  observations  elsewhere  than  in 
Dakota,  and  upon  a  woeful  lack  of  personal  knowledge  as 
to  our  true  artesian  supply.  The  sub-surface  supply,  while 
no  doubt  of  vast  extent  and  importance,  cannot  be  compared 
with  the  artesian  supply  in  its  extent,  universality,  volume, 
or  the  ultimate  economy  of  obtaining  it.  In  other  words— a 
given  volume,  in  a  given  time,  may  be  obtained  more  cheap- 
ly from  an  artesian  well  than  from  any  sub-surface  source 
by  whatever  means  it  may  be  secured. 

Notwithstanding  this  great  percentage  in  favor  of  the 
artesian  supply  the  other  sources  should  by  no  means  be 
neglected  or  overlooked.  The  value  to  the  state  of  the  phre- 
atic supply  will  be  beyond  calculation  if  the  people  will  but 
seek  its  development. 

As  before  stated  it  must  be  secured  by  mechanical  means; 
either  by  wind  or  by  steam  power.  Many  farmers— most  of 
them— cannot  raise  the  means  necessary  to  put  down  an 
artesian  well,  but  there  are  few  who  cannot  raise  enough  to 
put  in  a  pumping  plant  at  an  expense  of  but  a  few  hundred 
dollars. 

Reference  must  again  be  made  to  the  west  where  the 
manufacture  and  use  of  water-elevating  machinery  is  a  very 
large  and  rapidly  growing  industry.  Many  sections  of  coun- 
try cannot  be  supplied  by  water  taken  from  streams  by 
dutches,  so  the  water  must  be  elevated.  Thousands  of  wells 
have  been  put  down  in  the  several  \vestern  states  and  terri- 
tories from  which  the  water  will  not  fiow  so  it  must  be 
pumped.  This  industry  is  most  fully  developed  in  Califor- 
nia and  in  Colorado.  The  following  illustration  will  show 
the  comparative  economy  and  great  value  of  such  means. 

A  pumping  plant,  with  a  50  horse-power  engine,  will  raise 
7,500,000  gallons  of  water  to  a  height  of  10  feet  in  10  hours. 
This  amount  of  water  will  cover  28  acres  to  a  depth  of  one 
foot.  The  cost  of  the  plant  would  be  about  $3000.  One 
man  can  operate  it  with  about  one  ton  of  coal  per  day. 
While  so  large  a  plant  would  not  be  in  order  except  where 
the  supply  was  very  large,  a  plant  of  proportionately  less 


126 

capacity  and  cost  would  accomplish  proportionate  results. 
Many  places  may  be  found  from  which  enough  water  may 
be  pumped  to  irrigate  a  quarter  section  of  land. 

The  question  would  follow  as  to  the  means  to  be  used  in 
raising  the  water  to  the  surface  in  the  greatest  volume  and 
at  the  least  expense.  The  author  knows  of  no  better  means 
than  the  use  of  the  PULSOMETER  or  the  N  YE  VACUUM 
steam  pumps  which  possess  features  especially  adapting 
them  to  such  uses.  They  are  both  vacuum  pumps,  having  no 
pistons  or  machinery  to  wear  out  or  become  deranged,  are 
exceedingly  simple,  strong,  and  efficient,  and,  above  all,  are 
standard  the  world  over;  being  used  for  irrigation  purposes 
in  many  countries.  All  that  is  needed  is  the  pump,  a  steam 
boiler,  and  a  little  pipe.  There  are  hundreds  of  thresher 
engines  in  the  state  that  could  be  used  to  supply  steam,  and 
straw  being  used  as  fuel  the  expense  of  running  would  be 
but  nominal. 

A  No.  6  Pulsometer  pump  throwing  300  gallons  per  min- 
ute (18,000  gallons  per  hour)  would  cost  about  $225;  an  en- 
gine to  supply  steam  could  be  rented  during  its  period  of 
idleness  and  could  be  run  at  an  expense  of  but  $2  or  $3  per 
day  for  fuel  and  attendance.  Surely,  then,  here  is  a  most 
valuable  auxiliary  supply  in  the  irrigation  field  of  Dakota, 
and  a  means  of  utilizing  it  not  heretofore  presented  to  our 
people. 

The  cost  of  starting  the  plant— buying  the  pump,  pipe  and 
fittings,  digging  and  connecting  2  or  3  large  wells  and  get- 
ting the  boiler  need  not  cost  over  $1000,  yet  on  such  an  out- 
lay of  capital  enough  may  be  easily  made  in  any  one  year 
to  pay  the  cost  of  installation  and  enough  surplus  very  soon 
accumulated  to  warrant  the  sinking  of  an  artesian  well. 

The  increased  service  rendered  by  a  well,  as  the  result  of 
a  given  outlay  or  cost,  renders  that  means,  or  source  of  sup- 
ply, cheaper  in  the  long  run,  as  it  is  otherwise  the  basis  of 
more  extensive  operations;  but  if  the  greater  source  is  be- 
yond one's  financial  reach  then  by  all  means  grasp  at  the 
lesser  and  use  a  pump. 

WIND  MILLS. 

In  the  utilization  of  this  sub-surface  supply  the  agency  of 
wind  mills  may  be  made  to  play  an  important  part  and  this 
is  especially  true  in  this  country  of  almost  constant  winds. 
A  wind  mill  may  supply  water  for  a  very  considerable  area 
of  garden  and  orchard,  and,  if  reinforced  by  a  proper  water- 
elevating  device,  as  to  which  there  are  several  good  ones  in 
the  market,  and  also  a  storage  reservoir,  the  area  of  service 
could  be  very  greatly  extended  and  the  profit  of  the  farm 
greatly  increased.  This  means,  too,  deserves  the  careful 
consideration  of  our  farmers. 

Get  the  water  from  the  most  available  source  and  by  the 
most  efficient  means.  Only  get  it!  for  to  get  it  is  to 
acquire  a  competency. 


127 

Wherever  a  deposit  of  sand  or  gravel  is  found,  or  where 
wells  wherein  there  is  a  flow  or  current— in  and  out— are 
found,  there  is  to  be  found,  beyond  much  doubt,  a  supply 
which  would  abundantly  serve  the  land  upon  which  the 
supply  is  found.  Every  farmer  should  take  some  pains  to 
investigate  the  extent  and  character  of  his  sub -surf  ace  sup- 
ply with  a  view  to  its  future  utilization. 


Fig.  19. 

Showing   the    Pulsometer     Pump    as   set   for  taking   water   from     a 
stream  for  the  use  of  irrigation.    The  view  shows  the  extreme  simplicity 
of  the  plant  which  renders  it  especially  applicable  to  use  where  skilled 
labor  or  attendance   is  lacking.     Any  man  can  run  it  or  set  it  up. 
[See  next  page  and  page  244.] 


128 


Fig.  20. 

Fig.  20.  Shows  a  No.  6  Pulsometer  [capacity  18,000  gallons  per  hour] 
throwing  a  stream  46  feet  high  through  160  feet  of  3V£  inch  pipe,  into  a 
flume  on  top  of  the  bluff.  The  pump  irrigates  1400  fruit  trees,  uses  about 
Ys  cord  of  soft  wood  per  day  and  is  operated  by  an  Indain  boy.  The  plant 
is  in  Idaho. 

A  No.  9  pump,  on  a  lift  of  102  feet,  used  %  cord  of  wood  in  10  hours  and 
delivered  60,000  gallons  per  hour.  [See  page  244.] 


129 

LEVELING. 

It  would  require  more  space,  diagrams,  and  illustrations 
than  can  be  here  given  to  fully  treat  of  the  different  kinds 
of  levels,  their  adjustment,  use,  and  care;  and  to  describe 
and  illustrate  the  many  nice  points  in  the  art  of  leveling. 
Much  of  this  techincal  information  may  be  had  from  the 
pamphlets  issued  by  level  manufacturers  and  supplied  with 
the  instruments. 

Enough  will  be  given  to  convey  to  any  person  of  average 
intelligence  so  much  of  a  knowledge  of  the  art  as  is  neces- 
sary to  aid  in  doing  such  work  as  may  arise  about  the  farm, 
and  yet  such  as  it  would  not  pay  to  hire  an  engineer  to  do, 
even  if  one  were  to  be  had  at  call.  The  principle  of  level- 
ing is  to  reduce  the  inequalities  of  the  surface  to  a  uniform 
plane,  or  to  determine  the  position  of  a  succession  of  points 
with  reference  to  a  uniform  plane. 

DATUM  PLANE. 

It  is  apparent  from  this  that  some  plane  of  reference 
must  be  chosen  which  shall  be  that  to  which  all  other  points 
are  referred  Such  an  arbitrarily  selected  plane  is  called  the 
Datum  Plane,  or  plane  of  reference,  and  it  is  assumed  to  lie 
at  a  considerable  distance  below  the  surface  in  order  that 
all  points  referred  to  it  may  have  plus  (+)  elevations,  instead 
of  some  plus  (+)  and  some  minus  (— )  as  would  be  the  cas« 
if  some  portion  of  the  line  to  be  run  sank  below  the  level  of 
the  datum  plane. 

In  a  rough  or  mountainous  country  500  or  1000  feet  is 
taken  as  the  depth  of  the  plane  of  reference.  In  this  level 
country  100  feet  will  be  sufficient.  That  is,  in  starting  any 
piece  of  level  work  assume  that  the  starting  point  is  100  feet 
above  this  plane,  or  at  an  elevation  of  100;  then  proceed  to 
get  the  elevations  of  all  other  points,  whether  higher  or 
lower  than  the  starting  point.  Before  describing  the  opera- 
tion of  leveling  let  us  very  briefly  consider  the  level  or  level- 
ing instrument. 

THE  LEVEL. 

The  engineer's  level  is  a  telescopic  tube  carried  in  Ys  or 
collars,  and  having  a  long  level-bubble  tube  attached, 
mounted  on  a  horizontally  revolving  cross-head  which  is  ad- 
justed and  maintained  in  a  level  or  horizontal  position  by 
four  leveling-screws  attached  to  the  head  of  the  tripod  on 
which  the  instrument  rests.  Cross  hairs  in  the  tube  give  the 
exact  center  and  the  horizontal  line  of  sight.  Such  are  the 
main  features  of  a  level,  and  all  are  constructed  on  the  same 
general  plan. 

Some  instruments  are  made  with  a  less  powerful  and 
shorter  telescope,  with  fewer  parts,  lighter  weight,  and 
cheaper  in  price.  Levels  of  this  class  known  as  contractors, 
builders  or  architects  levels  are  far  cheaper  than  larg- 


130 

er  engineer's  levels  but  they  are  finely  constructed  and  good 
for  all  classes  of  work. 

A  still  cheaper  grade  of  level  is  the  so  called  "  drainage 
level "  which  is  made  for  the  express  purpose  of  farm  use 
inlaying  out  drains  and  ditches.  In* this  special  class  of 
instruments  there  is  a  wide  range  of  design  and  price,  the 
latter  ranging  from  $10  to  $30.  (The  manufacturers,  Buff 
and  Berger,  W.  and  L.  E.  Gurley,  and  Young  and  Sons, 
whose  advertisements  appear  herein,  are  leading  makers 
of  the  finest  instruments  and  will  supply  anything  in  the 
level  line.) 

A  $25  or  $50  instrument  will  do  good  work  and  last  a  life- 
time, if  properly  cared  for.  One  who  can  use  a  level  will 
soon  pay  the  cost  of  a  good  one  by  home-work.  If  no  good 
level  is  at  hand  a  simple  one,  for  rough  work,  may  be  made 
out  of  three  pieces  of  board  as  shown  in  Fig.  21. 

Take  two  pieces  of  nar- 
row board,  AB  and  AC,  of 
exactly  equal  length  and 
form  as  shown,  and  hav- 
ing a  span  from  B  to  C  of 
10  feet  [one  of  16^  foot 
span — 1  rod — may  be  more 
convenient.]  At  exactly 
equal  distances  from  A, 
measured  along  the 
sides,  attach  the  cross 
stick  D.  Fasten  on  the 
plumb  line  and  bob  P  and 
then  adjust  the  zero  point 
O  as  follows :  Drive  two 
stakes  in  the  ground,  as 
supports  for  the  level, 
having  one  of  them  2  or  3 
ins.  higher  than  the  other. 


Fig.  21.    A  simple  form  of  level. 


Set  the  foot  C  on  the  higher  stake  and  mark  upon  D  the  ex. 
act  point  where  the  line  cuts  the  edge— as  at  x.  Then  re- 
verse the  level,  end  for  end,  so  foot  B  is  on  the  higher  stake, 
and  again  mark  the  point  where  the  line  cuts  D — as  at  Y  . 
Draw  o  just  midway  between  these  lines.  Then  whenever 
the  plumb  line  cuts  this  o  mark  the  feet  B  and  C  are  <*n  a 
level.  In  one  foot  a  large  screw  may  be  set,  as  shown  in  the 
enlarged  view  at  S.  When  screwed  in  flush  the  level  is  set 
for  level  work  but  when  screwed  out  the  level  is  set  for  run- 
ning grades.  Thus— if  a  ditch  has  a  fall  of  1  foot  in  500 
feet  the  screw  would  be  turned  out  slightly  over  %  inch. 
The  level  would  be  set  50  times  in  the  500  feet  (it  having  10 
foot  span.)  so  -fa  of  1  foot  would  be  the  grade  for  each  setting. 

Such  a  tool  is  of  course  crude  but,  if  well  made  and  skill- 
fully handled,  it  will  yield  quite  good  results.  Other  simple, 
home-made  levels  are  frequently  described  but  this  is  as 
good  as  any.  Get  a  good  level  if  possible  and  learn  to  do 
-  good  work  with  it.  It  will  pay  you  if  you  do  much  irrigat- 
ing. 


THE  HOD. 


131 


The  level  rod  is  a  rod  of  dry  wood  from  8  to  12  feet  long, 
marked  into  feet,  and  tenths  and  hundredths  of  feet,  meas- 
uring upward  from  the  bottom  of  the  rod.  The  rod  may 
have  a  target  or  be  what  is  called  a  "self-reading"  rod.  The 
target  rod  has  the  graduations  cut  into  the  wood  and  the 
distances  indicated  by  figures  as  at  A,  Fig.  22,  the  feet  in 
large  red  figures  and  the  tenths  by 
smaller  black  figures.  The  Reveler 
views  the  cross  lines  on  the  target  and 
the  rod-man  takes  the  reading  as  indi- 
cated by  the  target.  (In  the  Fig.  the 
target  reads  4  feet) 

The  self-reading  rod  needs  no  target, 
for  the  leveler  takes  the  reading  from 
sight  at  the  instrument,  the  gradua- 
tions being  made  visible  by  painting  as 
shown  at  B,  Fig.  22.  Here  only  the 
feet  are  numbered,  the  smaller  gradu- 
ations not  requiring  it. 

Thus,  if  the  horizontal  hair  of  the 
level  cuts  at  the  following  points  on  the 
rod  the  reading  would  be  as  follows. 
Kefer  to  B  in  the  Fig. 

1=1.0  feet.        4=1.5  feet. 
2=1.05  "  5=1.75  " 

3=1.3    "  6=1.85  " 

The  reading  to  .05  feet  being  easily 
made,  and,  on  short  sights,  a  finer  read- 
ing may  be  approximated  although  a 
reading  of  less  than  .05  is  not  necessary 
except  in  very  fine  work. 
Such  rods  can  be  easily  and  accurate- 


Fig.  22, 
Leveling  Kods. 


ly  made  by  any  intelligent  person,  and 
at  a  cost  of  not  over  one  dollar.  The 
target  may  be  made  of  sheet  brass  or 
of  galvanized  iron. 

LEVELING. 

Leveling  is  very  simple  work,  and  the  keeping  and  reduction  of  level 
notes  equally  so.  The  first  thing  to  do  is  to  set  up  and  level  the  instru- 
ment and  to  select  the  HUB  or  starting  point.  The  form  of  note-keeping 
and  the  order  of  procedure  is  shown  on  the  next  page.  In  this  sample 
page  from  a  note-book  the  following  is  the  significance  of  the  letters  head- 
ing the  several  columns.  Stn.  =  Station  Number ;  B.  S.  =  Back  Sight 
[sometimes  called  +  Sight]  ;  H.  I.  =  Height  of  Instrument ;  F.  S.  =  Fore 
Sight  [sometimes  called  —  Sight] ;  Elev.  or  Ht.  =  Elevation  or  height  of 
Station ;  Rem.  =  Remarks. 

The  hub,  or  starting  point,  which  may  be  any  permanent  object,  or  a 
stake  driven  for  the  purpose,  is  assumed  to  have  an  elevation  of  100  feet 
which  fact  is  entered  in  the  note-book  as  shown.  The  rod  now  being  held 
on  this  hub  the  line  of  sight  of  the  instrument,  or  the  plane  passing 
through  its  center,  strikes  the  rod  4  feet  from  the  bottom.  Enter  this  un- 
der B.  S.  as  shown.  Now  if  the  hub  is  100  feet  and  the  instrument  reads  4 
feet  above  it.  the  center  of  the  instrument  is  evidently  on  a  plane  or  level 
of  104  feet  [so  that  Elev.  added  to  B.  S.  =  H.  I.  or  104  ft.]  The  H.  I.  being 
known  the  height  of  any  other  point  is  found  thus—.  The  rodman  goes 
to  station  1  and  the  leveler  reads  a  F.  S.  of  5.20,  which  he  enters  as  shown 
under  F.  S. 


132 
SAMPLE  PAGE  FROM  LEVELER'S  NOTE  BOOK. 


Stn. 

B.  S. 

H.I. 

F.  S. 

Elev. 

Rem. 

Hub 

4.00 

104.00 

100.00 

Hub  near  well. 

1 

5.20 

98.80 

3 

6.00 

98. 

3 

-  7.35 

103.80 

7.55 

8.80 

96.45 
95. 

T.  P.  [turning  point.] 
Hub,  at  barn. 

4 

2.60 

101.20 

5 

1.50 

102.30 

T.  P. 

6 

1.20 

103.50 

8.60 

94.90 

7 

2.10 

101.40 

1.70 

101.80 

If  the  instrument  is  on  a  level  of  104  ft.,  and  the  reading 
on  the  rod  at  Stn.  1  is  5.20,  it  is  evident  that  Stn.  1  is  5.20  ft. 
lower  than  the  instrument.  The  level  of  Stn.  1  is  therefore 
found  by  merely  subtracting  the  F.  S.  reading  on  that  Stn. 
(5.20)  from  the  H.  I.  (104)  =  98.80— which  enter  as  shown. 
In  like  manner  readings  are  taken  at  Stns.  2  and  3  which  re- 
sult as  shown  in  the  notes.  From  where  the  instrument 
now  stands  stn.  4  cannot  be  seen  so  the  level  is  moved  to  a 
new  position  from  which  stns.  4  and  5  may  be  seen.  Set  up 
and  adjust  as  before. 

The  rodman  having  staid  at  Stn .  3  the  leveler  now  takes  a 
B.  S.  reading  on  that  point.  The  reading  of  7.35  is  entered 
as  a  B.  S.  Stn.  3  (T.  P.,  or  turning  point)  having  an  Elev.  of 
96.45  and  the  B.  S.  equaling  7.35  their  sum,  or  103.80,  will 
give  a  new  H.  I.  or  plane  of  reference. 

Before  proceeding  to  take  the  level  ot  Stn.  4  the  leveler 
deems  it  best  to  take  level  on  some  new  hub  so  that  in  case 
the  original  hub  is  moved  or  destroyed  he  can  relocate  his 
work  from  the  new  hub.  The  rodman  sets  up  on  the  barn 
floor  and  the  leveler  reads  8.80  which  substracted  from  103.80 
=95  as  the  Elev.  of  the  barn  floor. 

He  then  proceeds  as  before  to  take  the  elevations  of  other 
stations  and  to  set  such  other  hubs  as  he  may  desire.  From 
this  explanation  may  be  drawn  the  whole  secret  of  leveling 
and  note  keeping. 

The  Elev.  of  any  starting  point  added  to  the  B.  S.  reading 
on  that  point  give  the  H.  I.  and  any  F.  S.  reading  subtracted 
from  the  H .  I.  gives  the  Elev.  of  the  point  on  which  the 
reading  is  taken.  Any  number  of  F.  S.  readings  may  be 
taken  from  one  setting  of  the  instrument  so  long  as  the 
range  of  sight  is  clear.  Thus,  the  instrument  may  be  set  at 
or  near  the  center  of  a  reservoir  and  the  levels  taken  at  all 
points  about  the  bank  without  moving. 

Aim,  however,  to  have  the  lengths  of  B  S  and  F  S  courses 
as  nearly  equal  as  possible  in  order  not  to  magnify  any 
slight  error  in  the  adjustment  of  the  instrument. 

Note  especially  one  fact— as  the  grade  or  level  runs  doivn 
the  target  or  reading  runs  up  on  the  rod;  that  is,  it  takes  a 
greatar  length  of  rod  to  reach  from  the  plane  of  the  instru- 


133 

ment  down  to  the  surface.    The  reverse  is  also  true— as  the 
surface  rises  the  reading  on  the  rod  lowers. 

TO  SET  A    LINE   OF  STAKES  ON    A    LEVEL. 

Set  one  stake  at  the  level  desired,  set  the  rod  on  this  stake 
and  clamp  the  target  on  the  reading .  Proceed  then  to  set 
other  stakes,  tapping  each  one  down  until  the  target— set  on 
the  stake— comes  into  the  plane  of  the  instrument. 

TO  SET  A   LINE   OF  STAKES  ON   ANY   GRADE. 

Set  and  get  level  on  first  stake.  Suppose  now  that  the 
grade  runs  down  at  the  fate  of  .1  ft.  in  50  feet  and  that  the 
stakes  are  25  feet  apart.  Move  the  target  up  on  the  rod  .05 
ft.,  clamp  it,  and  set  the  second  stake  by  it.  Move  it  up  05. 
again  and  set  the  third  stake ;  and  so  on  to  the  end.  Had 
the  grade  ran  up  then  the  target  would  have  been  set  down 
at  each  setting. 

If,  instead  of  setting  long  stakes  to  the  line  of  the  grade, 
short  ones  are  set,  the  level  of  each  short  stake  may  be  taken 
and  then  from  the  notes  the  height  of  the  grade-line  above 
or  below  each  stake  may  be  estimated  and  indicated. 

Many  complications  will  arise  in  any  extended  practice 
but  the  principle  is  the  same  and  the  specimen  notes  given 
embrace  the  secrec  of  the  whole  operation.  If  care  and 
judgment  are  exercised  fairly  good  work  may  be  done  by 
one  not  skilled  in  the  work. 

For  still  further  illustration  the  notes  are  here  given  of 
the  level-work  in  the  laying  out  of  a  reservoir.  A  reservoir 
of  but  1%  acres  will  be  taken  for  illustration.  Stake  out 
the  circumference,  on  the  center  line  of  the  top  of  the  bank, 
into  sections  of  50  feet  each  (except  where  otherwise  stated 
in  the  notes) — circumference  being  905  ft. 

LEVEL  NOTES  —LAYING  OUT  A  RESERVOIR- 


Stn. 

B.  S. 

H.I. 

F.  S. 

Elev. 

Height  to  Grade. 

Hub 

1 

5.2 

105.2 

5.0 

100.0 
100.2 

106.0 
5  8 

2 

5  5 

99.7 

6  3 

3 

6.2 

99.0 

7  0 

3+30 

7.6 

97  6 

8  4 

+60 

10.2 

95.0 

11  0 

+90 

7.5 

97.7 

8.3 

4 

6.6 

98.6 

7  4 

5 

4.2 

101.0 

5  o 

6 

o  o 

102.0 

4  0 

7 

4  4 

100  8 

5  2 

8 

4.8 

100.4 

5  6 

9 

4  8 

100  4 

5  6 

Stn  =  105  ft 
1 

5.0 

100.2 

5.8 

Set  up  near  the  center  and  proceed  to  take  the  level  of 
e  ach  stake;  first  having  set  a  reference  hub  at  some  conven- 


134 

lent  place  outside  of  the  reservoir,  the  height  of  which  call 
100  ft.,  which,  added  to  the  B  8  of  5. 2 =105.2= the  H  I.  The 
notes  show  a  gradual  descent  from  station  1  to  a  point  30  ft. 
beyond  stn.  3  at  which  point  there  is  a  sudden  descent  into  a 
shallow  "draw",  the  bottom  of  which  is  at  3+60.  Thence 
there  is  a  sudden  rise  to  30+90  and  then  a  gradual  rise  to 
stn.  6,  where  the  highest  point  is  reached,  and  thence  a  grad- 
ual fall  to  stn.  1  where,  on  a  reading  of  5.0,  the  level  is 
found  to  check  with  the  beginning  of  the  work. 

In  looking  over  either  the  F.  8.  readings  or  the  Elev.  re- 
sults one  may  readily  see,  in  the  imagination,  a  profile  of  the 
work  without  platting  it  on  paper.* 

Assume,  now,  that  the  top  of  the  bank  .will  be  4  feet  above 
the  highest  point,  at  stn.  6— the  elev.  of  which  is  102  ft., 
then  the  grade-line  will  be  on  a  level  of  106.  Enter  this  in 
the  last  column  as  shown.  It  is  apparent  that  the  height  of 
the  bank  at  each  stn.  will  be  the  difference  between  the  level 
of  that  stn.  and  the  level  of  the  grade-line;  therefore,  sub- 
tract the  height  or  elev.  of  each  stn.  from  the  grade-height 
(106)  and  the  remainder  will  be  the  height  of  the  bank  at 
that  stn.,  which  enter  as  shown  in  the  last  column. 

The  staking  out  of  the  toe  or  base  of  the  bank  on  the  in- 
side and  outside  may  now  be  done  since  the  height  and 
slopes  are  known.  The  inner  slope  being  2  to  1  and  the 
.  outer  slope  l^to  1  measure  off  from  each  stake,  toward  and 
from  the  center  of  the  reservoir  the  bottom  widths  occord- 
ing  to  the  height  of  the  bank  at  that  point  plus  %  the  width 
of  the  top  of  the  bank.  Thus— at  stn.  4.  the  height  being 

7.4  ft.,  the  distance  to  the  inner  toe  would  be  7.4x2=14.8+ 

2.5  (J£  top)=17.3  ft.     The  distance  to  the  outer  toe  would  be 
7.4x1.^=11.1+2.5=13.6  ft.,  a  total  width  of  30.9  feet. 

The  estimate  of  the  number  of  cubic  yds.  of  earth  in  the 
bank  may  be  done  with  sufficient  accuracy  by  assuming  the 
cross-section  to  be  level  and  the  height  of  the  bank  in  each 
section  as  a  mean  or  average  of  the  end  heights.  Thus,  the 
height  at  stn.  6  is  4  feet;  and  at  stn.  7  it  is  5.2  ft.  The  aver- 
age height  may  be  taken,  therefore,  as  the  height  of  the 
full  stn.,  4.0+5.2=9.2-^-2=4.6=average  for  100  ft. 

Get  area  of  section  of  this  height,  and  compute  cu.  yds. 
for  100  feet  as  explained  under  head  of  "  Keservoirs. "  Do 
the  same  for  each  stn.,  add  the  sums  to  get  the  total  cubic 
contents. 

This,  it  is  believed,  will  make  clear  what  is  really  a  very 
simple  operation  and  will  enable  any  farmer  to  do,  or  to  aid 
in  doing,  part  or  all  of  his  own  work. 

With  three  sticks,  a  ball  of  binding  twine,  a  few  stakes, 
and  a  hatchet,  with  a  little  good  judgment  and  care  thrown 
in,  any  farmer  may  do  in  two  hours  what  it  would  cost  him 
$5  to  $10  to  have  done— and  still  not  be  overcharged.  Do 
seme  level  practice,  if  only  for  exercise. 


1 

1    • 

2" 

_p 

; 

o 

(* 

-3 

jt 

4— 

- 

4t 

6" 

. 

-6 

0 

_ 
— 
__ 

. 

- 
• 
- 

9  : 

, 

10  —  : 
ll— 

12 

10 

INCHES 

TENTHS 

135 
Fig.23. 

DECIMAL  AND  DUODECIMAL  SCALES. 

TRUE  AND  APPARENT  LEVEL. 

Brief  mention  only  need  be  made  of 
the  difference  between  true  and  appar- 
ent level.  In  ordinary  leveling  opera- 
tions no  account  is  taken  of  the  curva- 
ture of  the  earth. 

True  level  is  a  water-level  which  is  the 
true  curvature  of  the  earth. 

Apparent  level  is  a  horizontal  plane 
tangent  to  the  plane  of  true  level  at  any 
point  and  extending  indefinitely  into 
space. 

In  leveling  the  sights  are  short  and 
constitute,  therefore,  a  succession  of  tan- 
gent planes  which  closely  approximate  a 
curve  of  true  level.  The  difference  be- 
tween a  curve  of  true  level  and  a  plane 
of  apparent  level  is  about  8  inches  per 
mile  [7.98  ins.  or  .667  ft.]  and  increases  as 
the  square  of  the  distance;  being 4  times 
8  inches  in  2  miles,  9  times  8  inches  in  3 
miles,  etc. 
MEASUREMENTS. 

Nearly  all  measurements  in  engineer- 
ing work  are  made  in  feet  and  decimals 
—tenths  and  hundredths— instead  of  in 
feet  and  inches.  This  is  especially  nec- 
essary in  leveling.  Table  Ko.  67,  show- 
ing the  decimals  of  a  foot  corresponding 
to  each  -fa  of  an  inch  will  be  of  conven- 
ience in  the  conversion  of  measurements 
from  one  unit  to  the  other.  For  ordin- 
ary work  the  decimal  corresponding  to 
the  nearest  half  or  quarter  inch  will  be 
close  enough.  To  aid  in  getting  this  at 
a  glance  Fig.  23  has  been  prepared  show- 
ing (in  >£  size)  a  foot  measure  divided 
into  inches  and  eighths;  and,  on  the  op- 
posite side  the  divisions  to  tenths  and 
hundredths.  This  will  be  of  much  use 
to  the  leveler  in  certain  work . 

Examples.—  6  inches  =  5  tenths. 

9       "       =75  hundredths. 

10       "       =83  " 

and          7  tenths  =8%  inches. 

25  hundredths  =  3  inches,  &c. 
The  scale  may  be  more  readily  used  than  a  table. 
The  unit  of  measurement  used  by  the  govern- 
ment in  surveys  of  the  public  lands  is  the  chain 
of  66  feet,— 4  rods— this  being  divided  into  100 
links  of  7.92  inches  each.  For  rules  as  to  the 
conversion  of  chains  and  links  to  feet,  yards,  &c., 
see ''Mensuration"  and  table  of  multipliers. 


13H 


VALUE  OF  WATER,  VALUE  OF  LAND 

AND    SIZE    OF    FARMS    UNDER  A    SYSTEM 
OF    IRRIGATION. 


VALUE  OF  WATER. 

Water  for  irrigation  has  a  double  value. 
First.    The  first  cost  of  getting  it  upon  the  land,  or  the 

value  of  the  Water  right. 
Second.    The  annual  rental  value. 

Table  No.  53,  on  the  opposite  page,  shows  statistics  as  to 
values,  etc.,  which  are  official  and  as  accurate  as  only  the 
Government  could  secure.  The  table  contains  much  of  value 
and  deserves  careful  study. 

The  first  cost  of  securing  a  water  supply  or  right  will  de- 
pend upon  the  supply,  the  distance  it  must  be  brought,  the 
manner  of  bringing,  etc.  All  the  expense  of  dams,  head- 
gates,  ditches,  flumes,  pipe-lines,  or  tunnels  must  be  born-by 
the  area  served,  so  all  these  expenses  enter  into,  and  form 
a  part  or,  the  first  cost  per  acre  of  a  water  right.  The  value 
of  the  right  being  such  an  amount  as  will  pay  all  the  ex- 
penses and  leave  a  proper  margin  of  profit.  This  value 
ranges  from  a  mere  nominal  price  to  $30  or  more  per  acre, 
but  averages  as  shown  in  the  table.  The  right  attaches  to 
the  land  and  passes  with  the  title  thereto.  Once  paid  for  it 
is  perpetual  as  a  right,  but  the  continued  enjoyment  of  that 
right  is  contingent  upon  the  performance  of  other  conditions 
— as  the  payment  of  an  annual  tax  for  the  use  of  the  water, 
or  the  performance  of  certain  labors  in  maintaining  the 
ditches. 

The  amount  of  the  value  of  the  water  right  may  usually 
be  considered  as  the  value  of  the  land,  for,  as  a  rule,  the 
land  has  little  or  no  value  without  the  right. 

As  touching  most  directlv  upon  the  value  of  well-waters 
reference  may  be  made  to  the  Gage  group  of  29  wells  near 
San  Bernardino,  California.  They  are  within  a  radius  of  1 
mile,  are  from  4  to  10  inches  in  diameter  and  have  an  aver- 
age daily  flow  of  about  33  miner's  inches,  (about  300  gallons 
per  minute)  or  a  total  of  954  inches,  (about  8600  gallons  per 
minute.)  One  inch  is  apportioned  to  5  acres  and  is  sold  as 
high  as  $250  an  acre,  or  $1250  an  inch.  The  average  price 
thereabouts  being  $1000  per  inch.  At  this  rate  the  total  flow 
is  worth  $954,000  and  it  will  water  nearly  5000  acres. 

Four  good  Dakota  wells  will  throw  more  water  and  will 
serve  more  land.  Such  being  the  case  one  Dakota  well  of 
2200  gallons  per  minute  would,  according  to  this  accepted 
California  estimate,  be  worth  $238,500.  (Continued on  P.  138.) 


137 
TABLE  NO.  53. 


OS    CO    OS    30  00  "^    C- 
OS    rH    £"•    lO  lO  OO    IO 

-        '°  t-'d        6 


183    S 


oa  ^o      TH 

CO  t-  00        CO 

^'  d      os 


I    <MCD 

I  ooo 


S        CD  CO  10        OS 
lO  CD  Oi         <?d 

T^'  d     oo* 


CO 
COO        00 


00 
5-3 


5oi§ 


f 

>-i  M 


rt  «s 

8sf 
5>- 


s 

CD 


10 

00* 


-H         OO 


CO 
00 


*"'•$•••:& 


CD        05 

00         CO 
•^          TH 


"  " 


-g  -S  So^  ^ 
^    «"C  rt  "^ 


^  0,0 


-1-J    ^ 


2 

0, 


£  a;  N  ^^  <u  c  ^ 
al  ^  '^         N   J3   O 

.^  S        uT'3  M  J! 


"9  >-s 
S)^ 


^5  5 

o  o 


££ 

W3     O 


C  00 

o  ^ 


I 


£ 
o 


138 

It  is  not  the  intention  to  place  such  values  on  wells  that 
can  be  sunk  for  $3000  or  $4000  yet  such  is  their  legitimate 
value  as  compared  with  values  elsewhere. 

Our  wells  possess  values  far  in  excess  of  their  cost,  and 
far  greater  than  even  their  owners  now  dream  of.  A  good 
well  is  really  a  fortune  to  its  owner. 

In  Oregon,  on  one  large  tract,  the  annual  charge  is  $3.00 
per  acre  for  1  foot  depth  of  water  (1  acre  foot)  to  be  used  in 
3  irrigations.  At  this  rate  a  Dakota  well  would  pay  its 
cost  in  two  years,  if  not  in  one.  In  other  states  the  annual 
charge  per  acre  foot  is  about  the  same,  but,  inasmuch  as  the 
crop  is  a  certainty  and  abundant  in  amount,  this  apparently 
high  tax  is  not  felt  as  at  all  burdensome. 

The  Dakota  irrigator  who  would  achieve  success  must 
abandon  the  false  idea,  which  many  farmers  entertain,  of 
getting  someting  for  nothing.  He  must  put  in  both  money 
and  labor,  and  considerable  of  each,  in  order  to  make  a  suc- 
cess of  irrigation.  Nor  need  he  be  discouraged ;  for  all  the 
advantage  is  on  his  side.  It  will  cost  less  here  to  secure  a 
water  right  than  in  almost  any  other  section  because  a  given 
volume  may  be  had  for  a  lesser  outlay. 

Again,  the  Dakota  water-right  is  also  a  water-power 
which  very  largely  increases  its  value.  It  is  not  subject  to 
periodic  fluctuations,  prior  rights  of  up-stream  claimants, 
and  such  other  uncertainties  and  annoyances  as  are  experi- 
enced under  other  systems.  It  is  perpetual,  is  under  perfect 
control],  may  be  put  to  many  uses  and  in  all  respects  has  a 
value  not  possessed  by  water  rights  in  other  sections  or  un- 
der other  systems 

The  cost  of  reservoirs,  ditches,  gates,  etc.,  is  not  a  part  of 
the  water  right,  but  a  tax  upon  the  land  in  its  preparation 
for  irrigation.  In  this  respect  also  Dakota  has  a  great  ad- 
vantage, for  her  gently  rolling  or  nearly  level  lands  require 
but  little  preparation  as  compared  with  the  heavy  work  of 
terracing,  checking,  diking,  ditching,  leveling  and  otherwise 
treating  the  land,  as  so  often  necessary  elsewhere. 

Finally,  as  to  the  ANNUAL  COST  of  water.  Where,  in 
other  states,  the  annual  cost  is  from  25  cents  to  $5  per  acre 
—averaging  over  $1— the  Dakota  average  will  be  but  a  few 
cents,  and  in  most  cases  nothing,  for  the  flow  of  the  well  be- 
ing continuous,  requires  no  attention  or  expense.  Once  ob- 
tained its  volume  comes  free. 

In  every  essential  particular  wherein  an  irrigation  system 
burdens  the  irrigator  with  expense—first  cost  of  water,  an- 
nual cost  of  water,  preparation  of  ground,  future  mainte- 
nance of  plant— he  who  irrigates  in  Dakota  bears  the  least 
burden;  has  the  greatest  advantage;  the  most  valuable,  con- 
trollable, and  diverse  right;  to  say  nothing  of  the  proximity 
to  the  best  and  largest  markets. 


139 

A  consideration  of  many  details  only  tends  to  strengthen 
and  confirm  this  conclusion  that  Dakota's  artesian  irriga- 
tion system  will  be  the  cheapest  and  the  best  of  the  many 
systems  developed"  in  this  country. 

The  experience  of  the  failure  years,  1888-1889-1890,  taken 
in  connection  with  the  results  obtained  by  the  great  crop  of 
1891  (See  table  No.  43  and  remarks  in  connection  therewith) 
prove  not  only  the  enormous  value  of  water  in  Dakota  but 
substantiate  the  estimate  of  duty  of  water  given  in  table 
16.  If  the  estimate  there  given  is  approximately  correct, 
and  the  annual  value  of  water  be  taken  to  be  but  $2  per  acre 
then  from  table  16  it  will  appear  that  a  well  of  1350  gallons 
per  minute  would  be  worth  $1950  per  year  or  fully  40  per 
cent  on  its  cost.  This  is  assumed  to  be  a  rental  value. 

To  the  owner  the  actual  value  would  be  the  net  value  of 
all  crops  raised  in  excess  of  the  average  yield  of  non-irriga- 
ted lands  in  his  neighborhood.  No  reasonable  person  will 
estimate  the  probable  average  yield  of  irrigated  wheat  at 
less  than  30  bushels  per  acre,  which  average  would  be  fully 
1 8  bushels  more  than  the  average  without  irrigation.  As- 
suming a  net  return  of  but  50  cents  per  bushel,  this  would 
give  to  the  water  a  value  of  $9  per  acre  to  the  owner;  or  an 
amount  sufficient  to  pay  the  full  cost  of  the  well  together 
with  the  cost  of  the  land,  in  one  year. 

This  is  not  an  exagerated  estimated  but  rather  an  under- 
estimate as  has  been  demonstrated  by  actual  experience. 

A  parallel  cannot  fairly  be  drawn  between  the  values 
either  of  water  or  of  land  as  between  the  fruit  growing 
lands  of  California  and  the  grain  fields  of  Dakota;  but  mak- 
ing all  needful  allowances  for  the  character  of  the  crops 
raised,  and  their  value  per  acre,  the  value  of  water  to  our 
grass  and  grain  fields  is  still  actually  far  beyond  the  amount 
which  even  sanguine  estimate  would  give  to  it. 

A  thousand  gold  mines  would  not  be  so  valuable  to  our 
people  as  are  these  artesian  waters.  Hasten,  therefore,  to 
develope  this  pent-up  wealth  which  awaits  the  opportunity 
to  flow  to  the  coffers  of  each  enterprising  claimant. 

VALUE  OF  LAND. 

One,  in  considering  the  relative  values  of  irrigated  and  un- 
irrigated  lands,  may  border  closely  upon  the  realm  of  the 
marvelous  while  yet  not  transgressing  the  bounds  of  cold 
facts,  for  it  is  truly  marvelous  that  the  worthless  deserts  of 
the  arid  west,  have,  within  a  few  years,  been  clothed  in  semi- 
tropical  luxuriance  through  the  agency  of  irrigation,  and 
have  been  raised  in  value  from  actual  zero  to  as  much  as 
$2000  per  acre.  It  is  but  a  few  years  since  California  and 
Colorado  were  known  only  as  great  mining  states.  To-day, 
through  the  agency  of  the  impounded  waters  of  the  moun- 
tain streams,  they  have  been  transformed  into  great  agricul- 


140 

tural  states;  the  harvest  of  the  golden  fruit  and  of  golden 
grain  having  long  since  superseded  in  value  the  harvest  of 
the  golden  metal.  Where  then  there  were  mining  camps 
now  there  are  prosperous  cities,  and  where  then  vice  reigned 
supreme,  now  peace  and  plenty  bless  the  community. 

Millions  of  acres  of  barren,  sage-brush  or  of  sand-flecked 
desert,  of  lava-beds  and  of  sun-parched  plains  have  been  re- 
claimed arid  are  to-day  the  most  valuable  and  productive 
lands  on  the  continent.  It  is  true  that  the  high  values  of 
$1000  per  acre  and  upward  are  usually  fancy  prices,  but 
many  thousands  of  acres  have  ready  market  values  of  from 
$50  to  $500  per  acre. 

Good  lands,  under  water,  the  ditching  and  like  preparation 
being  done,  are  worth  from  $50  to  $100  per  acre,  and  find 'a 
ready  market  at  these  figures . 

Any  piece  of  property  is  truly  worth  such  an  amount  as 
will  represent  the  principal  upon  which  a  fair  rate  of  interest 
can  be  permanently  earned. 

If  land  will  produce  annually  a  crop  which  will  yiWd  a  net 
income  of  $10  per  acre  that  land  is  worth  $100  per  acre  to  a 
man  who  demands  a  10  per  cent  investment;  or  $200  per 
acre  to  a  man  who  is  content  with  5  per  cent.  Such  values, 
and  only  such,  are  legitimate. 

The  remarkable  development  of  Southern  California  has 
been  due  almost  solely  to  irrigation .  As  an  illustration  of 
the  increase  in  property  values  may  be  cited  the  statistics 
relative  to  San  Diego  Co.,  which  may  be  taken  to  represent 
that  section  of  the  state. 

Real  Estate.  Improvements. 

1880  1890  1880  1890 

$1,307,302        $20,000,085  $341,948        $4,450,286 

While  no  corresponding  increase  can  be  expected  in  any 
Dakota  county  there  is  still  room  for  an  increase  in  value 
far  beyond  the  present  values.  Taking  Brown  Co.,  S.  D.,  to 
fairly  represent  the  two  Dakotas,  the  average  market  value 
of  the  lands  of  the  county  would  probably  not  exceed  $6  per 
acre.  An  increase  of  $5  per  acre  would  add  over  $6,000,000 
to  the  valuation  of  the  county  and  still  leave  the  lands  far 
below  their  actual  value. 

Such  a  change  in  the  ready  market  value  of  these  lands 
may  be  brought  about  within  two  years  if,  within  that  time 
it  can  be  shown  that  these  lands  can  be  made  to  produce 
from  25  to  50  bushels  of  wheat  to  the  acre,  no  matter  what 
the  season  may  be. 

No  doubt  exists  as  to  this  being  demonstrated— it  has  been 
already  in  Brown  Co.  and  in  other  counties  within  the  arte- 
sian basin. 

As  soon  as  the  foreign  land  purchaser  and  investor  learns 
of  the  wonderful  possibilities  of  this  artesian  basin  the  pre- 
sent land  owners  will  find  a  ready  market  for  their  surplus 


141 

holdings  at  prices  now  beyond  their  fairest  fancies.  What 
is  it  that  can  do  this  magic  act— the  creation  of  millions  of 
value  where  now  little  appears  ?  What  is  it  that  can  and 
will  do  for  Dakota  what  irrigation  has  done  for  our  sister 
states  ?  What  is  it  that  can  banish  poverty,  misfortune  and 
ruin  from  our  state  and  bring  riches,  prosperity  and  happi- 
ness in  their  place?  That  can  quench  the  thirst  of  our 
once  parched  prairies  with  a  perennial  draught  of  nature's 
purest  waters  ? 

ARTESIAN  WELLS! 

No  agency  is  so  pregnant  of  promise  for  the  welfare  of  the 
Dakotas  and  none  deserves  the  same  attention  as  the  de- 
velopment of  this  great  industry— artesian  irrigation.  It  is 
not  only  a  boon  to  him  who  puts  it  to  practice  but  to  the 
community  in  which  he  lives,  for  it  shows  to  the  world  the 
possibilities  awaiting  all  who  choose  to  engage  therein,  and 
fixes  to  our  lands  a  value  because  of  their  latent  possibilities 
for  successful  agricultural  development. 

The  author  has  heard  it  remarked,  but  recently,  by  a 
wealthy  eastern  man  who  owns  (perforce)  several  thousand 
acres  of  Dakota  lands,  but  possesses  no  knowledge  of  irriga- 
tion, that  if  artesian  irrigation  proves  to  be  what  it  is  claim- 
ed to  be  he  would  sink  several  wells  and  thus  trebble  the  value 
of  the  lands  which  today  he  would  sell  for  what  they  cost. 

No  doubt  there  are  scores  of  such  cases,  and  it  is  to  prove 
to  such  men  the  true  value  of  their  lands,  and  to  still  further 
interest  them  and  their  monied  friends  in  schemes  of  devel- 
opment that  every  effort  should  be  put  forth  to  demonstrate 
to  the  world  the  true  extent  and  value  of  the  latent  possi- 
bilities we  have  within  our  reach  and  control . 

Every  possible  publicity  should  be  given  to  every  truth, 
to  every  demonstrated  fact  touching  upon  the  well  or  irri- 
gation interests,  and,  by  reason  of  the  approaching  World's 
Fair  and  its  resultant  era  of  prosperity  and  commercial 
activity  every  possible  effort  should  be  made  to  push  the 
business  of  irrigation  at  home  and  a  knowledge  of  its  results 
abroad;  for  no  better  time  will  ever  come  for  Dakota  to 
enthrone  herself  in  the  good  will  of  the  capitalists  of  the 
world  and  regain  her  lost  prestige,  than  the  immediate 
future. 

The  farmers  and  the  business  men  of  the  state  should 
organize  and  prepare-  in  every  legitimate  way  to  promote 
this  all  important  industry,  for  the  success  or  failure  of  the 
state  depends  upon  it,  and  all  other  interests  pale  before  it 
in  importance  and  the  effect  upon  the  general  prosperity  of 
all  classes.  If  this  appeal  to  the  patriotic  home  enterprise 
of  Dakotans  shall  result  in  creating  any  .of  that  interest 
which  the  subject  warrants,  then  will  this  little  volume  riot 
have  been  issued  in  vain. 


142 
SIZES  OF  FARMS. 

A  word  of  caution  as  to  over-irrigation,  in  point  of  area, 
will  well-nigh  be  wasted  inasmuch  as  the  invariable  tendency 
is  to  attempt  to  irrigate  too  large  an  area.  A  few  unsuccess- 
ful attempts  to  irrigate  too  broad  an  area  will  convince  the 
farmer  that  a  lesser  area,  better  served  and  cultivated,  will 
yield  better  results. 

In  a  fruit-growing  country  an  area  of  5  or  10  acres  is 
enough  for  a  single  holding.  As  the  crop  is  changed  to 
vegetables,  grass,  or  cereals  the  area  which  may  be  advan- 
tageously cultivated  increases.  It  is  assumed  that  the  hold- 
ing is  worked  on  the  plan  of  the  average  farm— by  the 
farmer  and  his  family,  with  the  assistance  of  the  average 
amount  of  hired  help.  As  the  number  of  hands,  actively 
engaged  in  the  farm  labor,  increases,  so  may  the  area  treated 
be  increased.  The  character  of  the  land  to  be  cultivated— 
whether  it  be  easily  managed  or  the  reverse— will  likewise 
determine  the  area  which  a  given  service  of  labor  can  prop- 
erly manage;  as  will  also,  the  character  of  the  crops  raised. 

It  will  be  well  in  starting  out  to  thoroughly  treat  such  an 
area  as  the  supply  of  water,as  well  as  of  labor,  can  treat  to  the 
best  advantage.  In  short,  go  only  so  far  as  you  can  go  with 
thoroughness.  The  following  year  this  area  will  require  far 
less  attention  so  the  surplus  of  water  and  of  labor  may  be 
expended  in  an  extension  of  the  area  served,  until  the  max- 
imum shall  have  been  reached.  No  other  method  of  pro- 
ceedure  will  prove  satisfactory  unless  "  bonanza  "  methods 
are  adopted.  Table  No.  53,  of  statistics,  in  the 

3d,  4th,  5th  and  6th  lines,  shows  at  a  glance  the  results 
reached  in  7  other  states  as  to  areas  under  irrigation. 

What  there  is  shown  is  true  of  all  other  states  and  coun- 
tries, except  that,  as  the  country  becomes  older,  and  irriga- 
tion methods  are  improved,  the  duty  of  water  increased, 
and  more  care  and  labor  is  given  to  a  given  area,  the 
product  of  that  area  increases  and  a  lesser  holding  is  relied 
upon.  So  it  will  be  in  Dakota  after  the  irrigation  system  is 
more  general;  the  farms,  instead  of  becoming  larger  will 
become  smaller,  and  better  and  more  thorough  methods  of 
cultivation  will  be  practiced.  From  these  smaller  areas 
will  be  returned  a  larger  yield  and  one  as  certain  as  the 
order  of  the  seasons  and  as  bounteous  as  the  prosperity 
which  will  attend  them. 

"  Bonanza  "  farms  may  be,  and  no  doubt  are,  fine  things 
for  their  owners,  but  they  are  of  little  use  to  any  community. 
A  community  of  small  farms,  all  of  which  are  prosperous 
and  each  of  which  supports  in  plenty  a  family,  is  the  most 
truly  a  model  in  all  the  elements  which  enter  into  the  gen- 
eral prosperity,  wellf are  and  happiness  of  the  people.  So 
each  farmer  will  do  better  by  his  own  interests,  and  those 
of  his  neighbors,  if  he  seeks  to  place  his  present  holding 
under  more  thorough  cultivation  rather  than  to  extend  his 
holding  and  neglect  the  proper  cultivation  of  the  whole. 


143 


PHOTOGRAPHS. 

Any  good  engraver  can  engrave  a  picture  of  an  artesian 
well,  and— so  to  speak— can  doctor  it  up  to  show  according 
to  his  own  ideas  of  magnitude,  or  those  of  the  person  for 
whom  he  works,  which  ideas  may  far  exceed  the  facts . 

Not  so,  however,  with  a  photograph  or  any  picture  having 
a  photograph  as  iis  base— such  as  photo-engravings.  The 
camera,  with  the  quickness  of  light,  makes  a  record  true  to 
nature,  and  of  the  smallest  details;  a  record  with  which  the 
enthusiast  cannot  tamper;  which  none  can  question. 

The  importance  of  photographing  the  wells  of  the  state 
has  but  recently  impressed  itself  upon  the  leading  photog- 
raphers. Already  several  of  them  have  quite  fine  collections 
of  views  of  the  wells  in  their  neighborhood  and  take  pains 
to  secure  views  of  each  new  well.  Some  have  made  a  con- 
siderable profit  out  of  their  views,  for  a  fine  view  finds  a 
ready  sale  at  home  and  abroad.  Ere  long  the  sale  of  well 
views  will  form  an  important  item  in  the  income  of  Dakota 
artists.  A  photograph  of  a  well  needs  no  argument  back  of 
it;  it  tells  its  own  story;  is  its  own  best  witness  as  to  its 
truthfulness  to  nature,  and  convices  the  skeptic  who  would 
not  otherwise  accept  the  facts,  as  shown,  on  the  affidavit  of 
a  friend,  without  some  misgivings. 

Hence  the  importance  of  taking  photographs  and  giving 
them  a  wide  circulation.  They  are  unimpeachable  witnesses 
as  to  the  volume  and  power  of  our  wells  and  will  command 
respectful  attention  where  the  most  glowing  verbal  descrip- 
tion will  be  wasted  on  skeptical  ears. 

The  eastern  man  who  has  never  seen  a  flowing  well  cannot 
comprehend  the  nature  of  one  from  a  mere  verbal  descrip- 
tion; and  even  an  old  well  driller,  unacquainted  with  such 
great  wells,  will  laugh  in  his  sleeve  at  the  narrator  or  will, 
with  his  friend  the  capitalist,  say  "that  is  the  biggest 
Dakota  lie  I  have  heard  yet." 

Show  him  a  photograph,  however,  and  his  skepticism 
turns  to  wonder  and  amazement.  No  argument  will  prevail 
against  the  evidence  of  the  light,  and  the  capitalist  whose 
interest,  perchance,  has  been  solicited  will  turn  to  investi- 
gate or  to  invest  instead  of  turning  away  in  disgust  or  in 
wonder  at  the  stupendous  lying  abilities  of  the  Dakota  man. 

Enthusiasm  on  the  well  subject  is  ligitmate  and  laudable 
and  increases  as  one  sees  and  learns  more  of  this  wonderful 
power  and  supply.  Enthusiasm  is  still  further  heightened 
by  a  comparison  of  the  Dakota  wells  with  those  of  other 
sections  of  the  country.  Not  a  comparison  of  reports,  set 
in  cold  type,  but  a  comparison  of  lifelike  photographs. 
It  is  this  enthusiasm  that  should  be  fostered  by  every  resi- 
dent of  Dakota,  and  especially  by  every  photographer. 


144 

Every  person  and  corporation  should  lend  every  possible  aid 
to  the  photographer  in  his  effort  to  secure  good  views;  and 
the  photographer  in  his  turn  should  improve  every  oppor- 
tunity to  secure  views,  and  then  place  them  at  a  price  such 
as  will  enable  every  one  to  secure  a  supply  to  send  away. 

There  is  no  telling  what  one  will  find  its  way  into  the 
hands  of  some  man  who  will  invest  thousands  of  dollars  in 
wells  and  irrigation  projects  as  the  direct  result  of  having 
seen,  and  been  impressed  with,  a  photograph  of  a  well. 
Every  person  engaged  in  placing  irrigation  bonds,  or  the 
stocks  of  irrigation  companies,  should  have  a  collection  of 
the  best  views  in  the  state  and  every  eastern  bond-negotia- 
ting agent  should  be  similarly  supplied. 

Collections  of  well  views  could,  to  excellent  advantage,  be 
handsomely  framed  and  placed  in  the  lobbies  of  the  leading 
eastern  hotels  and  in  other  places  of  popular  resort.  Such 
exhibitions  would  be  seen  by  thousands  of  wondering 
and  admiring  spectators.  Thus  would  a  knowledge  of  the 
vast  possibilities  of  Dakota's  great  wells  be  spread  among 
a  class  of  people  who  could  not  be  reached  by  other  means. 

Thousands  of  views  could  in  this,  and  in  other  ways,  be 
placed  where  they  would  be  a  greater  advertisement  to  the 
state  at  large  than  any  other  that  could  be  made. 

A  lithograph  of  a  goddess,  of  an  eagle,  of  a  gapping  crowd 
of  emigrants,  or  of  a  chariot  procession  may  be  a  work  of 
art  but  it  can  be  of  little  value  to  the  people;  but  if  an  equal 
number  of  views  of  our  great  artesian  wells  were  scattered 
over  the  land  the  result  would  be  a  large  influx  of  people, 
seeking  to  share  the  undoubted  benefits  the  artesian  waters 
will  confer,  and  of  money  to  develop  an  industry  upon 
which  the  agricultural  success  of  this  agricultural  state 
depends.  Every  view  sent  out  should  have  attached  a  full 
and  ACCURATE  description  covering  as  many  as  possible 
of  the  following  points: 

Name,  or  location  of  the  well. 

When  drilled,  and  by  whom. 

Depth,  in  feet. 

Pipe,  size  in  inches  all  the  way,  or  at  top  and  at  bottom. 

Volume,  discharge  in  gallons  per  minute  when  opened 
and  full  size,  and  if  possible,  when  discharging 
through  smaller  sized  openings. 

Pressure,  in  pounds  per  sq.  inch,  when  closed,  and,  if 
possible,  when  streams  of  different  sizes  are 
being  discharged. 

Discharge,  height  of  throw  or  discharge  of  streams  of 
different  sizes,  or  the  horizontal  distance  to 
which  the  streams  are  thrown. 

Temperature, 
Character  of  water,  hard,  soft,  clear,  muddy,  palatable,  &o. 

Use  to  which  the  supply  is  put. 


145 

If  several  views  are  had  of  one  well  note  which  view  is 
shown  and  what  it  is— whether  it  is  the  4  inch  stream  or  the 
6  inch  stream,  &c. 

Without  this  description  the  view  has  little  value,  and  the 
value  even  then  rests  largely  on  the  exact  TRUTHFUL- 
NESS of  the  description  given.  It  is  poor  policy,  to  say  the 
least,  to  exaggerate  as  to^the  volume,  pressure,  discharge,  or 
the  size  or  height  of  the  stream  shown. 

If  an  exceptionally  fine  negative  is  secured  a  duplicate 
should  be  made,  for  some  accident  may  befall  the  first  one 
or  it  may  become  gradually  worn  out  through  use. 

The  author  was  desirous  of  having,  as  a  prominent  feat- 
ure of  this  little  volume,  a  series  of  photogravure  views  of 
the  leading  wells  of  the  state  but  the  expense  would  have 
been  greater  than  the  circumstances  of  its  issue  would  per- 
mit, so  the  idea  was  abandoned  for  the  present  edition. 
Should  the  book  meet  with  such  favor  as  to  warrant  another 
edition  this  feature  will  be  added  thereto.  Through  the 
courtesy  of  the  leading  photographers  of  the  state  the  author 
has  secured  a  collection  of  all  the  views  of  the  wells  thus  far 
photographed. 

A  list  is  added(on  the  next  page)of  the  photographers  hav- 
ing views,  their  addresses,  and  a  list  of  the  views  they  have 
for  sale.  This  will  be  a  great  boon  to  the  general  public 
who  will  thus  be  informed  as  to  what  views  may  be  had,  and 
where  to  secure  them.  By  this  means  it  is  to  be  hoped  a 
large  trade  in  views  may  be  worked  up  and  the  photograph- 
ers thereby  stimulated  to  the  work  of  taking  all  such  views 
as  may  be  possible  within  their  territory.  The  importance 
of  cultivating  this  mutual  interest  is  far  reaching  and  it  is 
hoped  that  added  interest  will  be  taken  in  well  photography 
because  of  the  great  good  that  may  flow  therefrom  to  the 
people  of  all  parts  or  the  state. 


The  author  with  pleasure  acknowledges  the  courtesy  of 
views  received  from  the  following: 
S.  W.  Fergusson,  Bakersfield,  Cal.    5  Kern  Co.  wells. 
Wm.  Kennish,  Wilmington,  N.  C.    Ponce  de  Leon  well,  Fla. 
H.  C.  Humphrey,  North  Yakima,  Wash.    Yakima  wells. 
And  from  all  the  photographers  listed  on  page  146. 


146 


WHERE  TO  BUY  WELL  PHOTOGRAPHS. 

Photographs  of  Dakota's  famous  artesian  wells  may  be 
secured  by  writing  to  the  following  Photographers. 


Photographer. 

Address. 

List  of  Views. 

Grade. 

B.  W.  Burnett. 

These  views 
are  among 
the  best  in 
the   state. 

Tyndall, 
S.  D. 

Springfield  well,  6  inch  stream. 

4*              4         "                         " 

"      and  mill. 
Niobrara,  Neb.  well,  8  in.  stream 
"        "    2  derrick  v'ws 
Zinnert        well    3  in.  stream. 
"     Shadeland  farm 

A 
A 
A 
A 
B 
A 
A 

D.  O.  Root. 

City  well 
views  are  the 
best  i  n   the 
state. 

Woonsocket, 
S.  D. 

Large,  of  City  well,  4  in.  stream. 
2  small  "    " 
Hinds  well,  vertical  stream, 
horizontal  &  vert.  s. 

A 
A 
B 
B 

L.  Janousek. 

Yankton, 
S.  D. 

Brick  yard  well,  stand-pipe  view. 
"     boiler  view. 

A 
A 

P.  C.  Anderson 

Redfield, 
S.  D. 

Water  works  display  view. 

B 

Quiggle  & 
Johnson  . 

Rapid  City, 
S.  D. 

Doland  well  6  inch  stream. 

44         g         U 

A 
A 

J.  Q.  Miller. 

Aberdeen, 
S.  D. 

Railway  well. 
Beard          "    6  inch  stream. 
"    4    " 
Williams    "    4    " 

B  . 
A 
A 
B 

Chas.  H. 
Newcombe. 

These  views 

Huron, 
S.  D. 

Day  well,  vertical  stream. 
"       "    double 
Dity     "    water  works  display. 
10  views  of  irrigated  farm. 
Jlisdon  well,  8  in.  derrick  view. 

A 
A 
A 
B 
A 

are  also  very 
nice. 

2  " 
6  "    clear 

5  " 
4  « 

2i'4 
Kerr               3  views. 

A 
A 
A 
A 
A 
A 
A 

Note:  In  the  above  list 
ative  values  of  the  views, 
ceilence  or  interest  and  B 


A  and  B  refer  to  the  grade  or  rel- 
A  indicates  a  view  of  special  ex- 
a  view  of  lesser  value. 


147 

EXPLANATION  OFTABLE  OF  TANGENTS  &  COTANG'S-P-l*8 

I.  Required  the  tangent  of  the  angle  65°  20'  1 

In  the  first  column  of  degrees  find  65,  then  pass  horizont- 
ally across  to  the  column  headed  20'  where  find  2.17749  as  the 
tang,  required.  If  the  number  of  minutes  in  the  given 
angle  is  not  found  in  the  head  of  the  table  proceed  as 
follows: 

II.  Required  the  tangent  of  the  angle  65   26 '  f 

Proceed  as  before  to  get  the  tangent  for  65°  20',  which  is 
the  next  lowest  number  of  minutes  given  at  the  head  of  the 
table.  This  leaves  an  excess  of  6  minutes.  At  the  right 
hand  of  the  table  under  the  head  of  k<  Prop .  (Proportional) 
parts  to  1  "  find  169  in  the  same  line  with  65  at  the  left 
side.  169  x  6=1014  which  added  to  2.17749,  the  tang,  for  65° 
20',  equals  2.18763  as  the  required  tangent.  (This  gives  a  suffi- 
ciently approximate  Tangent  for  ordinary  use.  Exact  Tangent =2. 187  55 .) 
COT  A  N  G  E  N  TS  are  taken  from  the  table  by  taking  the  degrees  from 
the  column  of  degrees  at  the  right  side  and  the  minutes  from  those  indi- 
cated at  the  foot  of  the  table,  thus — 

III.  Required  the  cotangent  of  the  angle  24   40  ? 

In  the  right  hand  column  of  degrees  find  24°,  then  pass 
horizontally  across  the  table— to  the  left— to  column  haying 
40  at  the  foot,  and  find  2.17749  as  the  cotang.  required. 
From  this  it  is  seen  that  the  tang,  of  any  angle  is  the  cotang. 
of  the  complement  of  that  angle,  for  65°  20 '+24°  40' =90°. 
Proceeding  as  at  II— 

IV.  Required  the  cotangent  of  angle  24°  34'$ 
(The  complement  of  65°  26'.) 

Obtain  cotangt.  for  24°  30'  which=2.19430  and  from  col- 
umn of  prop,  parts  find  169,  which  multiplied  by  4,  for  the 
4'  we  have  in  excess  of  30 ',=676.  \Vhere,  in  finding  the 
tangent,  this  correction  was  added  it  is  now  subtracted,  in 
finding  the  cotangent.  2.19430  minus  676=2.18754 
The  exact  cotangent  =  2.18755. 

USE   OFTABLE   OF  TANGENTS- 

Tangents  are  used  principally  in  determining  heights  and  distances  by 
means  of  angles.  Refering  to  Fig.  11,  page  93,  suppose  a  surveyor's  tran- 
sit to  be  set  at  A,  so  the  angle  FAE  can  be  measured,  and  suppose  that 
angle  to  be  38°  40  .  The  line  EF  is  the  tangent  of  the  angle  FAE.  From 
the  table  we  find  the  tangent  of  the  angle  38°  40'  to  be  .80020  which  mul- 
tiplied by  100,  the  distance  from  A  to  F,=80.02  or 80  ft.  as  the  height  of  the 
stream. 

Proceed  in  like  manner,  for  any  other  angle,  to  multiply  the  horizontal 
distance  by  the  tabular  tangent  to  get  the  length  of  the  tangent.  Suppose 
a  2  ft.  rule  is  used  to  measure  the  angle,  as  described  on  page  158,  and 
that  the  opening  of  the  rule  is  8  inches— which  cor- 
responds to  an  angle  of  38°  57'— and  that  the  joint 
is  100  feet  from  the  well.  We  find  from  the  follow- 
ing table  that  the  tang,  for  38°  57  =.80855  whichXlOO 
=80.85.  In  this  simple  way  the  height  of  a  stream 
may  be  determined  within  a  foot  or  less. 

So,  too,  in  measuring  horizontal  distances  to  in- 
accessible points,  as  across  a  stream.  Suppose  it 
is  desired  to  measure  the  distance  A  B,  Fig.  24,  be- 
tween points  on  opposite  sides  of  a  river,  across 
which  measurements  cannot  be  carried.  From  A 
lay  off  a  right  angle  BAC  and  measure  A  C  any 
suitable  length,  say  350  feet.  From  C  measure  an- 
gle A  C  B  which=60°  5  —then  tang,  of  60°  5'= 
Fig.  24.  1.73805which  X 350=608.3  ft ,  the  distance  from  A  to  B 


148 

TABLE  NO.  78. 

See  explanation  of  table  on  page  147. 
NATURAL,  TANGENTS. 


Prop 

Deg. 

0' 

NX 

2W 

30' 

40' 

50' 

Deg. 

parts 

tor 

o 

00000 

00291 

00582 

00873 

01164 

01455 

01746 

89 

29 

1 

01746 

02036 

02328 

02619 

02910 

03201 

03492 

88 

29 

2 

03492 

03783 

04075 

04366 

04658 

04949 

05241 

87 

29 

3 

05241 

05533 

05824 

06116 

06408 

06700 

06993 

86 

29 

4 

06993 

07285 

07578 

07870 

08163 

08456 

08749 

85 

29 

5 

08749 

09042 

09335 

09629 

09923 

10216 

10510 

84 

29 

6 

10510 

10805  !  11099 

11394 

11688 

11983 

12278 

83 

29 

7 

12278 

12574 

12869 

13165 

13461 

13758 

14054 

82 

30 

8 

14054 

14351 

14648 

14945 

15243 

15540 

15838 

81 

30 

9 

15838 

16137 

16435 

16734 

17033 

17333 

17633 

80 

30 

10 

17633 

17933 

18233 

18534 

18835 

19136 

19438 

79 

30 

11 

19438 

19740 

20042 

20345 

20648 

20952 

21256 

78 

30 

12 

21256 

21560 

21864 

22169 

22475 

22781 

23087 

77 

31 

13 

23087 

23393 

23700 

24008 

24316 

24624 

24933 

76 

31 

14 

24933 

25242 

25552 

25862 

26172 

26483 

26795 

75 

31 

15 

26795 

27107 

27419 

27732 

28046 

28360 

28675 

74 

31 

16 

28675 

28990 

29305 

29621 

29938 

3025-5 

30573 

73 

32 

JI 

30573 

30891 

31210 

31530 

31850 

32171 

32492 

72 

32 

18 

32492 

32814 

33136 

33460 

33783 

34108 

34433 

71 

32 

19 

34433 

34758 

35085 

35412 

35740 

36068 

36397 

70 

3;} 

20 

36397 

36727 

37057 

37388 

37720 

38053 

38386 

69 

33 

21 

38386 

38721 

39055 

39391 

39727 

40065 

40403 

68 

34 

22 

40403 

40741 

41081 

41421 

41763 

42105 

42447 

67 

34 

23 

42447 

42791 

43136 

43481 

43828 

44175 

44523 

66 

34 

24 

44523 

44872 

45222 

45573 

45924 

46277 

46631 

65 

35 

25 

46631 

46985 

47341 

47698 

48055 

48414 

48773 

64 

36 

26 

48773 

49134 

49495 

49858 

50222 

50587 

50953 

63 

36 

27 

509.53 

51319 

51688 

52057 

52427 

52798 

53171 

62 

37 

28 

53171 

53545 

53920 

54296 

54673 

55051 

55431 

61 

38 

29 

55431 

55812 

56194 

56577 

56962 

57348 

57735 

60 

38 

30 

57735 

58124 

58513 

58905 

59297 

59691 

60086 

59 

39 

31 

60086 

60483 

60881 

61280 

61681 

62C83 

62487 

58 

40 

32 

62187 

62892 

63299 

63707 

64117 

64528 

64941 

57 

41 

33 

64941 

65355 

65771 

66189 

66608 

67028 

6745! 

56 

42 

34 

67451 

67875 

68301 

68728 

69157 

69588 

70021 

55 

43 

35 

70021 

70455 

70891 

71329 

71769 

72211 

72654 

54 

44 

36 

72654 

73100 

73547 

73996 

74447 

74900 

7535-5 

53 

45 

37 

75355 

75812 

76272 

76733 

77196 

77661 

78129 

52 

46 

38 

78129 

78598 

79070 

79544 

80020 

8049X 

80978 

51 

47 

39 

80978 

81461 

81946 

82434 

82923 

83415 

83910 

50 

49 

40 

83910 

84407 

84906 

85408 

&5912 

86419 

86929 

49 

50 
52 

41 

86929 

87441 

87955 

88473 

88992 

89515 

90040 

4* 

CO 

42 

90040 

90569 

91099 

91633 

92170 

92709 

93252 

47 

Do 

43 

93252 

93797 

94345 

94896 

95451 

96008 

96569  i   46 

55 

44 

96569 

97133 

97700 

98270 

98843 

99420 

1.00000 

45 

57 

Deg. 

«X 

40' 

3W 

207 

10' 

0' 

Deg. 

NATURAL  COTANGENTS. 


149 
TABLE  NO.  79— Continued. 


NATURAL  TANGENTS. 


Prop 

Deg. 

0' 

10' 

20' 

30' 

4(y 

50> 

Ucg. 

parts 

tol* 

45 

1,00000 

1.00583 

1.01170 

1.01761 

1.02355 

1.02952 

1.03553 

44 

59 

46 

1.03553 

J.  04158 

1.04766 

1.05378 

1.05994 

1.06613 

1.07-237 

43 

61 

47 

1.07237 

1.07864 

]  .08496 

1.09131 

1.09770 

1.10-414 

1.11061 

42 

63 

48 

1.11061 

.11713 

1.12369 

1.13029 

1.1*694 

1.14363 

1.15037 

41 

66 

49 

1.15037 

.15715 

1.16398 

1.17085 

1.17777 

1.18474 

1.19175 

40 

69 

50 

1.19175 

.19882 

1.20593 

1.21310 

1.22031 

1.22758 

1.23490 

38 

72 

51 

1.2*190 

.24227 

1.24969 

1.25717 

1.26471 

1.27230 

1.27994 

as 

75 

52 

1.27994 

.28764 

1.29541 

1.30323 

1.3U10 

1  31904 

1.3.704 

37 

78 

W 

132704 

.33511 

1.34323 

1.35142 

135968 

136800 

1.37608 

36 

82 

54 

1.37638 

1.38484 

1.39336 

1.40195 

1.41061 

1.41934 

1.42815 

35 

86 

5-5 

1.42815 

1.43703 

1.44598 

1.45501 

1.46411 

1.47330 

1.48256 

34 

90 

56 

1.482-56 

1.491JH) 

1.50133 

1.510*4 

1.52043 

1.53010 

1.53987 

33 

95 

57 

1.539H7 

1.54972 

1.55966 

1.56969 

1.579H1 

1  59002 

1.60033 

32 

100 

58 

160033 

1.61074 

1.62125 

1.63185 

1.64256 

1.65337 

1.66428 

31 

107 

59 

1.66428 

1.67530 

1.68643 

1.69766 

1.70901 

1.72047 

1.73205 

30 

113 

60 

1.73205 

1.74375 

1.75556 

1.76749 

1.77955 

1.79174 

1.80405 

29 

120 

61 

1.80405 

1.81649 

1.82906 

1.84177 

1.85462 

1.86760 

1.88073 

ft 

128 

62 

1.88073 

1.89400 

1.90741 

1.92098 

1.93470 

194858 

1.96261 

2i 

136 

68 

1.96261 

1.97680 

1.99116 

2.00569 

2.02039 

2.03526 

2.05030 

£6 

146 

M 

2.05030 

2.06553 

2.08094 

2.09654 

2.11233 

2.12832 

2.14451 

25 

157 

65 

2.14451 

2.16090 

2.17749 

2.19430 

2.21132 

2.22857 

2.24604 

24 

169 

66 

2.24004 

2.26374 

2.28167 

2.29984 

2  31826 

2.33693 

2.35585 

23 

183 

S7 

2.35585 

2.37504 

2.39449 

2.41421 

2.434.'2 

2.45451 

2.47509 

22 

199 

68 

2.47509 

2.49597 

2,51715 

2.53865 

2.56046 

2.58261 

2.60509 

21 

217 

69 

2.60509 

2.62791 

2.65109 

2.67462 

2.69853 

2.72281 

2.74748 

20 

235 

70 

2.74748 

2.77254 

2.79802 

2.82391 

2.85023 

2.87700 

2.90421 

19 

261 

71 

2.90421 

2.93189 

2.96004 

2.98868 

3.01783 

3.04749 

3.07768 

18 

289 

72 

3.07768 

3.10842 

3.13972 

3.17159 

3.20406 

3.23714 

3.27085 

17 

322 

73 

3.27085 

3.30521 

3.34023 

3.37594 

3.41236 

3.44951 

3.48741 

16 

360 

74 

3.48741 

3.52609 

3.56557 

3.60588 

3.64705 

3.68909 

3.73205 

15 

407 

75 

3.73205 

3.77595 

3.820a3 

3.86671 

3.91364 

3.96165 

4.01078 

14 

464 

76 

4.01078 

4.06107 

4.11256 

4.16530 

4.21933 

4.27471 

4.33148 

13 

534 

77 

4.33148 

4.38969 

4.44942 

4.51071 

4.57363 

4.63825 

4.70463 

12 

621 

78 

4.70463 

4.77286 

4.84300 

4.91516 

4.98940 

5.06584 

5.14455 

11 

732 

79 

5.14455 

5.22566 

5.30928 

5.39552 

5.48451 

5.57638 

6.67128 

10 

876 

80 

5.67128 

5.76937 

5.87080 

5.97576 

6.08444 

6.19703 

6.31375 

9 

1068 

81 

631375 

6.43484 

6.56055 

6.69116 

6.82694 

6.96823 

7.11537 

8 

1331 

82 

7.11537 

7.26873 

7.42871 

7.59575 

7.77035 

795302 

8.14435 

7 

1708 

83 

8.14435 

8.34496 

8.55555 

8.77689 

9.009R3 

9.25530 

9.51436 

6 

2270 

81 

9.51436 

9.78817 

10.0780 

10.3854 

10.7119 

11.0594 

11.4301 

5 

3168 

85 

11.4301 

11.8262 

12.2505 

12.7062 

13.1969 

13.7267 

14.3007 

4 

4728 

86 

14.3007 

14.9&4 

15.6048 

16.3499 

17.1693 

18.0750 

19.0bli 

3 

7806 

87 

19.0811 

20.2056 

21.4704 

22.9038 

24.5418 

26.4316 

28  6363 

2 

88 

28.6363 

31.2416 

34.3678 

38.1885 

42.9641 

49.1039 

57.2900 

89 

57.2900 

68.7501 

85.9398 

114.589 

171.885 

343774 

cc 

0 

Deg. 

SO" 

40' 

30' 

20' 

10' 

0' 

DCS 

NATURAL  COTANGENTS. 


150 

MENSURATION. 
WEIGHTS,  MEASURES  AXD  USEFUL  NUMBERS. 

AVOIRDUPOIS  OR  COMMERCIAL  WEIGHT. 

16  drachms  =  1  ounce    =  437.5  grains. 
16  ounces     =  1  pound    =  256  drachms  =  7000  grains. 
28  pounds     =  1  quarter  =  448  ounces. 

4  quarters  =  1  cwt.        =  112  pounds. 
20  cwts.         =  1  ton         =  2240  pounds  (long  ton.) 
2000  pounds     =  1  short  or  commercial  ton. 

APOTHECARIES    WEIGHT. 

20  grains      =  1  scruple. 

3  scruples  =  1  drachm  =  60  grains. 

8  drachms  =  1  ounce      =  480     •'         =  24  scru. 

12  ounces    =  1  pound     =  5760     '         =  288    "    =  96  drms. 

LONG    MEASURE. 

12  inches  =  1  foot. 
3  feet        =  1  yard     =       36  inches. 
16H    "  =1  rod       =     198      " 

160  rods        =  %  mile    =  31680      "        =  2640  feet. 
320    "  =lmile      =63360      "        =5280    " 

3  miles     =  1  league. 

A  palm  =  3  ins.    A  hand  =  4  ins.    A  span  =  9  ins. 
A  fathom  =  6  ft. 

GUIMTER'S  CHAIN. 

7. 92  inches    =  1  link. 

100  links       =  1  chain    =     4  rods  =     22  yards  =     66  feet. 
80  chains    -  1  mile      =320    "     =1760    "       =5280    " 

SQUARE  MEASURE. 


144       sqi 

9 
100 
30.25 
160 
16 
10 
640 

lare  inches 
feet 

yards 
rods 

chains 
acres 

_       £±       -t     

=  1  square  foot. 
=  1              yard. 
=  1      "        (architects 
=  1     •*'       rod. 
=  1      "        acre. 
=  1      u       chain. 
=  1      "        acre. 
=  1      "        mile. 

measure.) 
i  ,-, 

43,560  sq.  ft.  =  1  acre  =  208.71  ft.  on  each  side. 
A  circular  acre  is  235.504  ft.  in  diameter. 

MEASURES  OF  VOLUMES. 

LIQUID     MEASURE. 

(See  also  Page  151.} 

4  gills        =  1  pint      =  16  ounces. 
2  pints      =  1  quart    =    8  gills      =  32  ounces. 
4  quarts   =  1  gallon  =  32    k'         =8  quarts. 
31£  gallons  =  1  wine  barrel. 
63       '•       =1  hogshead. 

DRY     MEASURE. 

2  pints  =  1  quart. 

4  quarts  =  1  gallon  =     8  pints . 

2  gallons  =  1  peck      =16    "        =8  quarts. 

4  pecks  =  1  bushel  =  64    "        =32      "        =8  gallons 


151 
MENSUKATIOX,  continued. 


CUBIC   MEASURE. 

172s  cubic  iuches  =  1  cubic  foot. 

27    "        feet      =  1    "       yard  =  46,656  cu,  in. 

Note— A  cubic  foot  contains  2200  cylindrical  ins.,  33)0  spherical  ins.,  or 
6600  conical  inches. 


LIQUID   MEASURES. 

Giving  approximate  sizes  of  measures  to  contain  given  quantities  of 
liquid. 


em 

Half  pint 

Pint 

Quart 


Diam.  ins.  Height. 
1%  3 

2^4  3% 

3l/2  3 


Gallon 
2  gallons 

8 
10 


Diam.  ins.  Height. 
7  t> 

12 


14 
14 


12 
15 


A  cylinder  1  ft.  in  diameter  and  1  ft.  high  contains 


.02909  cubic  yards. 
.7854       "      feet. 
1357.1712       "      inches. 
.6311U.  S.  dry  bushels. 


5.876  U.  S.  gallons  -  48.96  Ibs. 


2.524U.  S.  dry  pecks. 
20. 196  U.  S.  dry  quarts. 
40. 392  U.  S.  dry  pints. 
23.50   U,  S.  liquid  quarts. 


A  box  24 
"  24 
"  16 
"  12 


SQUARE  BOX  MEASURE. 

X  16    inches  square  and  23  inches  deep  contains  a  barrel. 

y2        " 
1  bushel. 
yt    " 
Ipeck. 
.1  gaUon. 
i/2       " 
1  quart. 


X  16 
X  16% 

x  11*4 

X  8H 
X  8*4 
X  4% 
X  4& 


14 

8 
8 
8 
4 
4 
4 


MISCELLANEOUS 

A  CUBIC  FOOT  is  Equal  to 

1728  cubic  inches. 

.037037  cubic  yard. 

7.48052  liquid  gallons  (of  231  cu.  ins.) 

6. 42851  U.  S.  dry  gallons. 

.803564  U.  S.  bushels  (of  3150.42  cu.  in.) 

3.31426  U.  S.  pecks. 

3300.23  spherical  inches. 

.23748  U.  S.  liquid  barrel  of  3iy2  gals. 

62.425  pounds  of  pure  water  (approximately  62 V£  Ibs.) 

A  CUBIC  YARD  is  Equal  to 

27  cubic  feet . 

46,656  cubic  inches. 

21.69623  U.  S.  bushels  (struck.) 

201.974  U.  S.  gallons. 

A  GALLON  is  Equal  to 

231  cubic  inches. 

8.3216  pounds  of  water  (by  some  authorities  8.3383)  8^  Ibs. 

.1:3368  cubic  foot. 

A  cylinder  7  inches  in  diam.  and  6  inches  high. 

A  cube  6.1358  inches  on  a  side. 


152 
MENSURATION,  continued. 

OF  SQUARES,    RECTANGLES  AND   CUBES. 

The  area  of  any  parallelogram  =  length  X  width. 

Area  of  square  =  square  of  one  side. 

The  side  of  a  square  equal )      (  diameter  X  .88623,  or 

in  area  to  a  given  circle   )      (  circumference  X  .2821. 
To  find  side  of  inscribed  square  X  diameter  by  .  7071 . 
Area  of  inscribed  square  =  square  of  radius  X  2. 
The  side  of  a  square  X  1.128  =  diameter  of  an  equal  circle. 
Side  of  square  =  square  root  of  its  area. 

Side  of  square  =  square  root  of  Yz  the  square  of  the  diagonal. 
The  side  of  a  square  =the  diagonal  X  .707107  or  •+•  1.41421 
Side  of  square  X  1.51967=side  of  equilateral  triangle  of  equal  area. 
The  diagonal  =  the  sq.  root  of  twice  the  square  of  a  side. 
The  diagonal  =  side  X  1.41421 
The  length  of  a  rectangle  =  area  -4-  breadth. 
The  4  angles  of  any  quadrilateral  =  4  right  angles. 
Any  two  adjacent  angles  of  any  parallelogram  —  2  right  angles. 
The  contents  of  a  cube  =  length  X  breadth  X  height. 
The  length  of  the  side  of  a  cube  =  the  cube  root  of  its  contents. 

OF  TRIANGLES   AND   POLYGONS. 

The  area  of  any  triangle    =  j  %$£*»%  Ste'. OT 

rpk      u       »t  t4  _  f  half  the  product  of  the  2  sides  and 

i  the  natural  sine  of  the  contained  angle. 
The  complement  of  an  angle  =  its  defect  from  a  right  angle  (90°) 

'    supplement    "          "       —     "        "        "      two  right  angles  (180°) 
The  3  angles  of  any  triangle  —  2  right  angles. 
Area  of  trapszoid  =  altitude  X  Y*  the  sum  of  the  parallel  sides. 
Area  of  trapezium  =  divide  into  2  triangles  and  and  find  their  area. 
Area  of  equilateral  triangle  =  square  of  a  side  X  .433. 

(   sum    of   its   sides    X    perpendicular 

Area  of  any  regular  polygon  —  K   from  center  to  one  side  and  product 
( divided  by  2, 

OF  CIRCLES. 

DIAMETER  X  3.14159  =  circumference.         (commonly,  3.1416) 
X    .88623  =  side  of  equal  square. 
X    .7071    =  "  inscribed  square, 

squared  X  .7854  =  area  of  circle . 
=  circumference  -t-  3.14159  (3.1416). 
=  side  of  equal  square  -*-  .8862. 

"  inscribed  square  •+•  .7071. 

=  v'area  -*-  .7854. 

=  circumference  X  0.3183. 

X  7  and  product  -*-  22. 
=1.12837  X  square  root  of  the  area. 
=  as  355  is  to  113  so  is  circumference  to  diameter. 
CIRCUMFERENCE  -+-  3.1416  =  diameter. 
=  diameter  X  3.1416. 
=  3.5446  X  square  root  of  area. 
.=  as  113  is  to  355  so  is  diameter  to  circumference. 
AREA  =  square  of  diameter  X  .  7854. 

"  circumference  X  .07958. 
'    =  yz  diameter  X  Yz  circumference. 
•*    =  square  of  radius  X  3.1416. 

"     =  ^  areas  of  circles  are  to  each  other  as  the  squares  of  their 
~   (  diameters. 

Continued  on  next  page. 


153 


MERSURATION,  continued. 

Doubling  the  diameter  of  a  circle  increases  the  area  4  times. 
X  side  of  «iTO 


Diameter  of  circle  of  equal  priphery  as  square  =  side  X  1.2732. 
Side  of  square  of  equal  periphery  as  circle  =  diameter  X  .7854. 
Diameter  X  1.3468  =  side  of  an  equilateral  triangle  of  equal  area. 
Length  of  arc  =  number  of  degrees  X  .017453  X  radius. 

f  From  area  of  outer  circle  take  the  area  of 

1  inner  cicle,  remainder  =  area. 
Area  of  circular  ring  =  '-{  OR 

I  Sum  of  diameter  X  difference  of  diameters 

Land  product  X  .7854. 
Area  of  sector  of  circle  =  length  of  arc  X  V&  radius. 

Surface  of  cylinder  equals  circumf  .  X  length  +  area  of  two  ends. 


Contents 
Surface  of  sphere 
Contents       " 
"       of  widge 
pyramid 
or  cone 

The  square  of  the  diam.  of  a  sphere  X  3.1416  =  its  surface. 
The  product  of  the  two  axes  of  an  eclipse  X  .7854  =  its  area. 
The  sq.  rt.  of  V&  the  sum  of  the  squares  of  the  two  diameters  of  an 
elipse  X  3.1416  =  its  circumference. 


area  of  end  X  length . 
diameter  X  circumf. 
cube  of  diam.  X  .5236. 
area  of  base  X  Vz  altitude. 

[area  of  base  X  34  altitude. 


USEFUL     MULTIPLIERS. 

Note :  The  converse  is  obtained  by  dividing  instead  of  by  multiplying. 


Lineal  feet 

X        .00019 

— 

miles. 

yards 

X        .000568 

— 

Square  inches 

X        .00695 

-2 

square  feet. 

feet 

X         .111 

—  : 

"      yards. 

;<       yards 

X        .0002067 

-s 

acres. 

Acres 

X        .4840 

— 

square  yards. 

Cubic  inches 

X        .00058 

= 

cubic  feet. 

"     feet 

X        .03704 

S3 

yards. 

Circular  inches 

X        .00546 

= 

square  feet. 

Cylindrical  inches 

X        .0004546 

= 

cubic       '* 

feet 

X        .02909 

se- 

';     yards. 

Links 

X        .22 

ts 

yards. 

'• 

X        .66 

— 

feet. 

Feet 

X      1.5151 

= 

links. 

Square  feet 

X      2.2957 

— 

square  links. 

Width  in  chains 
Cubic  feet 

X      8. 
X      7.48052 

= 

acres  per  mile. 
U.S.  gallons. 

inches 

X        .004329 

= 

Ct                     <i 

Cylindrical  feet 

X      5.874 

= 

i»              <( 

inches 

X        .0034 

= 

((                       U 

U.  S.  gallons 

X         .133679 

IT 

cubic  feet. 

U.  S. 

X  231. 

= 

"      inches. 

Cubic  feet 

X        .8036 

— 

U.  S.  bushels. 

U.  S.  bushels 

X      1.2446 

— 

cubic  feet. 

Ibs.  avoirdupois 

X        .00045 

= 

tons  (2240  Ibs.) 

Cu.  ft.  water 

X    62.425 

ac 

Ibs.  avoir. 

X    62.37925 
268.8  gallons  of  water  =  1  ton. 

Ibs.  (according 

to  Haswell.) 

35.88  cu.  ft.    " 

=  1    " 

A  column  of  water  12  inches  high  by  1  inch  diameter  =  .341  Ibs. 

154 

MISCELLANEOUS  NOTES. 


CORN  AND  HOGS. 

A  bushel  of  corn  will  make  10H  Ibs.  of  pork,  gross.    Then : 

When  corn  costs  Pork  costs 

12H  cents  per  bushel  ll/2  cents  per  pound. 


Jones  &  Laughlin. 


TABLE  NO.  54. 

TABLE  OF  TIME. 


New. 


Time. 

Days. 

Hours. 

Minutes. 

Seconds. 

1  minute            — 

60 

1  hour                — 

60 

3600 

1  day                  — 

24 

1  440 

86400 

1  week                = 

7 

168 

10080 

604800 

1  civil  month    = 

28 

672 

40320 

2  419  200 

1  month 

30 

720 

43200 

2592000 

1  month             = 

31 

744 

44640 

2678400 

2  months            = 

60 

1440 

86400 

5184000 

3      " 

90 

2160 

129600 

7776000 

6      •' 

180 

4320 

259  200 

15  552  000 

1  year                = 

365 

8765 

525948 

31  556  829 

1  year                 =  365  ds.,  5  hrs.,  48  min.,  49T75  sec. 

1  year                =    52  weeks,  1  day,  5  h.,  48  m.,  49&  sec. 
(  1  month  of  28  or  29  days  (Feb.) 
1  year                 =  <  4  months  of  30  days. 
(7      "          "31      " 

UA  Solar  Day  is  the  time  between  two  successive  solar  noons,  or 
transits  (passages)  of  the  sun  over  the  meridian  of  a  place.  These  inter- 
vals are  not  of  equal  length  all  the  year  around.  The  average  length  of 
all  the  solar  days  is  called  the  Mean  Solar  Day;  and  is  the  same 
as  the  common  civil  day  of  24  hours  of  clock  time.  Civil  noon  is 
at  12  o'clock ;  but  solar,  or  apparent  noon,  may  be  about  14*4  min.  before ; 
or  1634  min.  after  12  correct  clock  time.  A  Siderial  Day  is  the  inter- 
val between  two  passages  of  the  same  star  past  the  range  of  two  fixed  ob- 
jects ;  and  is  the  precise  time  required  for  one  complete  revolution  of  the 
earth  on  its  axis.  The  sideral  day  never  varies ;  but  is  always  equal  to  23 
hours,  56  minutes,  4.09  sec.,  so  that  a  star  will  on  any  night  appear  to  set, 
or  to  pass  the  range  of  any  two  fixed  objects,  3  min.,  55.91  sec.  earlier  by 
the  clock  than  it  did  on  the  night  before,  so  that  the  number  of  sideral 
days  in  a  civil  year  is  1  greater  than  that  of  the  civil  days. 

An  Astronomical  Day  degins  at  -noon,  and  its  hours  are  counted 
from  0  to  24.  In  comparing  it  with  the  civil  day,  the  last  is  supposed  to 
begin  at  the  midnight  before  the  noon  at  which  the  first  began." 

Example :  Nov.  15  (civil  day)  begins  at  midnight ;  while  Nov.  15  (astro- 
nomical day)  does  not  begin  until  12  hours  later,  i.  e.  at  noon  of  Nov.  15, 
civil  day. 

9  A.  M.  of  civil  day  =  21  o'clock  of  artronomical  day. 

3P.M.  «    "        »     =    3      " 


155 
TABLE  NO.  55. 

TABLES  OF  WAGES. 

WAGES  PER  HOUR,  AT  DIFFERENT  RATES  PER  DAY. 

On  basis  of  10  hours  to  the  day.  New. 


TIME. 

\\ 

rAGES    PEI 

I  DAY. 

1.50 

1.75 

2.00 

8.25 

2.50 

3.00 

4.25 

V6  hour. 

.07 

.08 

.10 

.11 

.12 

.15 

.21 

1        * 

.15 

.17 

.20 

.22 

.25 

.30 

.42 

2 

.30 

.35 

.40 

.45 

.50 

.60 

.85 

3 

.45 

.52 

.60 

.67 

.75 

.90 

1.27 

4 

.60 

.70 

.80 

.so 

a.  oo 

1.20 

1.70 

5 

.75 

.87 

1.00 

1.12 

1.25 

1.50 

2.12 

Q 

.90 

1.05 

1.20 

1.35 

1.50 

1.80 

2.55 

7         * 

1.05 

1.22 

1.40 

1.57 

1.75 

2.10 

2.97 

8 

1.20 

1.40 

1.60 

1.80 

2.00 

2.40 

3.40 

9 

1.35 

1.57 

1.80 

2.02 

2.25 

2.70 

3.82 

1    Da* 

W 

V» 

2.00 

4.00 

2.25 

4.50 

2-50 

5.00 

3.00 

6.00 

4.25 

8.50 

3 

4.50 

-5.25 

6.00 

6.75 

7.50 

9.00 

12.75 

4         * 

6.00 

7.00 

8.00 

9.00 

10.00 

12.00 

17.00 

5 

7.50 

8.75 

10.00 

11.25 

12.50 

15.00 

21.25 

6 

9.00 

10.50 

12.00 

13.50 

15.00 

18.00 

25.50 

7 

10.50 

12.25 

14.00 

15.75 

17.50 

21.00 

29.75 

34     * 

.38 

.44 

.50 

.56 

.62 

.76 

1.06 

*4     • 

1.12 

1.31 

1.50 

1.68 

1.-87 

2.25 

3.18 

By  combination  of  rates  given,  amounts  per  hour  at  other  rates  may  be 
quickly  found. amounts  at  2.25  +  1.50  equal  amount  at  3.75  etc. 

WAGES  PER  DAY,  AT  DIFFERENT  RATES  PER  MONTH,  AND  ON 
BASIS  OF  DIFFERENT  NUMBER  OF  DAYS  IN  THE  MONTH. 

Rate  per  day,  at  following  rates  per  month. 


ll 

$ 
20 

25 

30 

a5 

40 

45 

50 

55 

60 

75 

80 

90 

100 

26 
28 
30 
31 

.77 
.71 
.67 
.65 

.96 
.89 
.83 

.81 

1.15 
1.07 
1.00 

.97 

1.34 
1.25 
1.17 
1.18 

1.54 
1.43 
1.33 
1.29 

1.73 
1.61 
1.50 
1.45 

1.92 
1.79 
1.67 
1.62 

2.12 
1.96 
1.83 

1.78 

2.31 
2.14 
2.00 
1.94 

2.89 
2.67 
2.50 
2.42 

3.08 

2.85 
2.67 

2.58 

3.46 
3.21 
3.00 
2.90 

3.85 
3.57 
3.33 
3.23 

It  is  the  practice  among  most  large  mercantile  conserns  and  corpora- 
tions, and  railway  companies,  to  pay  on  the  basis  of  26  days  to  the  month, 
•that  being  the  average  number  of  working  days.  All  government  em- 
ployees are  paid  on  substantially  the  same  basis. 

WAGES  PER  HOUR,  AT  DIFFERENT  RATES  PER  MONTH,  AND  ON 
BASIS  OF  26  DAYS  TO  THE  MONTH. 


Time. 


Rate  per  hour,  at  following  rates  per  month. 


20 

25  |  30 

35 

40 

45 

50 

60 

75 

90 

1  hour. 

.08 

.10 

.12 

.14 

.15 

.17 

.19 

.23 

.28 

.34 

2  hours 

.16 

.19 

.  ?,3 

as 

.31 

.34 

.38 

.46 

.57 

.69 

3 

.23 

.29 

.35 

,42 

.46 

.51 

.57 

.69 

.86 

1.03 

4 

.31 

.38 

.46 

.55 

.61 

.69 

.76 

.92 

1.15 

1.38 

5 

.39 

.48 

.58 

69 

.77 

.86 

.96 

1.15 

1.44 

1.73 

6 

.46 

.57 

.69 

.82 

.92 

1.03 

1.15 

1.38 

1.72 

2.06 

7 

.54 

.67 

.81 

95 

1.07 

1.21 

1.34 

1.61 

2.01 

2.42 

8 

.62 

.76 

.92 

1.08 

1.23 

1.38 

1.53 

1.84 

2.30 

2.76 

9 

.69 

.86 

1.04 

1.21 

1.38 

1.55 

1.72 

2.07 

2.59 

3.11 

1  day. 

.77 

.96 

1.15 

1.34 

1.54 

1.73 

1.92 

2.31 

2.89 

3.46 

156 


AREA  OF  FIELDS. 

TABLE  NO.  56. 

SHOWING  SIZES  OF  A  ONE  ACRE  FIELD,  THE  WIDTH  ADVANCING 
BY  5  FEET.  New. 


Wide 

Long 

Wide 

Long 

Wide 

Long 

Wide 

Long 

Wide 

Long 

ft.l 

43560 

45 

968 

90 

484- 

135 

322.7 

180 

242 

5 

8712 

50 

971.2 

95 

458.5 

140 

311.1 

185 

235.5 

10 

4356 

55 

792 

100 

435.6 

145 

300.4 

190 

229.3 

15 

2904 

60 

726 

105 

414.9 

150 

290.4 

195 

223.4 

20 

2178 

65 

670.2 

110 

396 

155 

281 

200 

217.8 

25 

1742.5 

70 

622.2 

115 

378.8 

160 

272.3 

205 

212.5 

30 

1452 

75 

580.8 

120 

363 

165 

264 

208.71 

208.71 

35 

1244.6 

80 

544.5 

125 

348.5 

170 

256.3 

1! 

40 

1089 

85 

512.4 

130 

335.1 

175 

248.9 

A  square  acre  . 

This  table  is  near  enough  for  all  practical  purposes.  If 
the  exact  size  is  required  to  a  second  decimal  place,  or  the 
length  corresponding  to  any  width  not  given  in  the  table, 
divide  43,560  (the  number  of  sq.  ft.  in  1  acre)  by  the  given 
width.  Thus:  what  will  be  the  length  of  a  field  of  one  acre 
the  width  being  183.7  ft.  ? 

43,560-^-183.7=237.12  ft.  long. 

In  like  manner  obtain  the  area  or  the  size  of  any  rectangu- 
lar field.  Had  it  been  desired  to  find  the  length  of  a  field  of 
17  acres  the  width  of  which  was  to  be  183.7  ft.  then  43,560 
would  be  multiplied  by  17  and  the  product  divided  by  the 
given  width. 

If  the  length  and  breadth  are  given  and  the  area  is  wanted 
divide  the  total  area  in  square  feet  (the  product  of  the 
length x  by  the  breadth)  by  43,560  and  the  answer  will  be  in 
acres.  In  the  above  table  the  doubling  of  any  one  dimen- 
sion doubles  the  area— 1089  ft.  long  by  80  ft.  wide  would 
contain  2  acres;  but  doubling  both  dimensions  increases  the 
area  4  times— 2178  long  by  80  ft.  wide=4  acres. 

TABLE  NO.  57 

SHOWING  SQUARE  FEET  IN  DIFFERENT  AREAS.        New. 


Acres. 

Square  feet  of  area  . 

Acres. 

Square  feet  of  area. 

% 

21780 

60 

2  613  600 

1 

43560 

80 

3484800 

2 

87  120 

100 

4356000 

3 

130  680 

120 

5  227  200 

4 

174240 

160 

6  969  600 

5 

217800 

240 

10  454  400 

6 

261360 

320 

13  939  200 

7 

304920 

480 

20  908  800 

8 

348480 

640 

27  878  400 

9 

392040 

800 

34848000 

10 

435600 

960 

41  817  600 

20 

871200 

1120 

48  787  200 

40 

1  742  400 

1280 

55  756  800 

157 
AREA  OF  FIELDS,  continued. 


1  Acre 
square      a 

;;    # 

circular 

«       l/z 

-re 

- 

10        square  chains. 
208.71    feet  on  a  side. 
147.581    " 
104.355    "        "        *4 
235.50       '    in  diameter. 
166.52      "      " 
117.75      "      " 

AREA  OF  RAILWAY  RIGHT  OF  WAY. 

50  feet  wide  contains      .1148  acres  to  100  feet  of  length. 
100    "        "  .2296      •'      "  100    "      " 

50    "        "  •'  6.06         "      "  1  mile     '• 

100    "       "  "         12.12     •    *•      "1    •* 

If  the  field  is  of  irregular  form  divide  it  up  into  smaller 
rectangular  or  triangular  pieces,  estimate  the  area  of  each 
in  cu.  ft,  add  these  areas  and  divide  the  total  by  43,560  to 
get  the  area  in  acres.  The  division  may  be  made  by  platting 
the  outline  of  the  field  on  paper,  then  making  the  divisions 
desired,  and  taking  the  measurements  of  the  parts  from  the 
scale  of  the  drawing. 

If  the  measurement  has  been  made  in  chains  and  links 
point  off  5  places  from  the  right  of  the  product  obtained,  to 
get  the  area.  Example.  —  A  field  is  8  chains  and  20  links 
wide  and  10  chains  and  45  links  long—  what  is  the  area  in 
acres  ? 

8.20x10.45=8.56900.  (5  places  being  pointed  off.)  Multi- 
ply the  5  figures  cut  off  (.56900  in  this  case)  by  4  and  again 
point  off  5  figures,  the  remainder  is  roods;  multiply  the  5 
figures  cut  off  by  4  and  again  cut  off  5  figures  to  get  a  re- 
mainder in  rods  or  perches.  In  the  above  example  56900x4 
=2.27600  and  27600  X  4=  1.10400.  Therefore,  above  field 
equals  8  acres,  2  roods  andl.103  rods  in  area. 
TABLE  NO.  58. 


NUMBER  OF  HILLS  ON  ONE  ACRE. 


Haswell. 


Ft.  apart 

No. 

Ft.  apart 

No. 

Ft.  apart 

No. 

Ft.  apart 

No. 

1 

11/2 

2 
2l/6 
3 
8H 
4 
44* 

43560 
19360 
10890 
6969 
4840 
3556 
2722 
2151 

E* 

6/2 

\A 

8K 

1742 
1440 
1210 
1031 

889 
775 
680 
692 

9 

9V4 

10 

10*72 

12 
13 
14 

15 

538 
482 
435 
361 
302 
258 
223 
193 

16 
17 

18 
20 
25 
30 
35 
40 

171 
151 
135 

108 
69 
48 
35 
27 

PRISM 01  DAL  FORMULA. 

A  prisrnoid  is  a  solid  bounded  by  six  plain  surfaces  only 
two  of  which  are  parallel. 

To  find  the  contents  of  a  prismoid,  add  the  areas  of  the 
two  parallel  sides  and  four  times  the  area  of  a  section  taken 
midway  between  and  parallel  to  them,  and  multiply  this 
sum  by  $  of  the  perpendicular  distance  between  the  paral- 
lel sides. 

This  formula  is  used  in  the  calculation  of  quantities  of 
excavation  and  embankment  on  railroads,  canals,  etc. 


158  TABLE  NO.  58^. 

From  Trautwine's  "Civil  Engineer's  Pocket  Book." 


ANGLES. 


Approximate  Measurement  of  Angles. 

(1)  The  four  fingers  of  the  hand,  held  at  right  angles  to  the  arm  and 

at  arm's  length  from  the  eye,  cover  about  7  degrees.  And  an  angle  of  7°  corre- 
sponds to  about  12.2  feet  in  100  feet ;  or  to  36.6  feet  in  100  yards ;  or  to  645  feet  in  a 
mile. 

(2)  By  means  of  a  two-foot  rule,  either  on  a  drawing  or  between  dis- 
tant objects  in  the  field.    If  the  inner  edges  of  a  common  two-foot  rule  be  opened 
to  the  extent  shown  in  the  column  of  inches,  they  will  be  inclined  to  each  other 
at  the  angles  shown  in  the  column  of  angles.    Since  an  opening  of  ^  inch  (up 
to  19  inches  or  about  105°)  corresponds  to  from  about  ]^°  to  1°,  no  great  accuracy 
is  to  be  expected,  and  beyond  105°  still  less;  for  the  liability  to  error  then  in- 
creases very  rapidly  as  the  opening  becomes  greater.    Thus,  the  last  y&  inch  cor- 
responds to  about  12°. 

Angles  for  openings  intermediate  of  those  given  may  be  calculated  to  the 
nearest  minute  or  two,  by  simple  proportion,  up  to  23  inches  of  opening,  or 
about  147°. 

Table  of  Angles  corresponding  to  openings  of  a  2-foot  rule. 

(Original). 

Correct. 


Ins. 

Deg.  min. 

Ins.  Deg.  min. 

Ins. 

Deg.  min. 

lus. 

Deg.min. 

Ins. 

Deg.min. 

Ins.  Deg.  min. 

/4 

1  12 

4J4  \  20  24 

8)4 

40  IS 

2/4 

61  23 

16J4 

85  H 

20M  '  H5  5 

1  48 

21 

40  51 

62  5 

86  3 

116  12 

Yt 

2  24 

K    21  37 

y* 

41  29 

y* 

62  47 

y* 

86  52 

y*  in  20 

3  00 

22  13 

42  7 

63  28 

87  41 

118  30 

% 

3  36 

% 

22  50 

% 

42  46 

% 

64  11 

H 

88  31 

%    119  40 

4  11 

23  27 

43  24 

64  53 

89  21 

20  52 

1 

4  47 

5 

24  3 

9 

44  3 

3 

65  35 

17 

90  12 

21      22  6 

5  23 

24  39 

44  42 

66  18 

91  3 

23  20 

i/ 

5  58 

i/ 

25  16 

M 

45  21 

i/ 

/ 

67  1 

14    91  54 

M  !  24  16 

6  34 

25  53 

45  59 

67  44 

92  46 

25  54 

i£ 

7  10 

i^ 

26  30 

i£ 

46  38 

\s 

68  28 

y2 

93  38 

y% 

27  14 

7  46 

27  7 

47  17 

69  12 

94  31 

28  35 

«x 

8  22 

a/ 

27  44 

H 

47  56 

% 

69  55 

%  i  95  24 

H  j  29  59 

8  58 

28  21 

48  35 

70  38 

96  17 

31  25 

2 

9  34 

6 

28  58 

10 

49  15 

14 

71  22 

18 

97  11 

22 

32  53 

10  10 

29  35 

49  54 

72  6 

98  5 

34  24 

!£ 

10  46 

M 

30  11 

y* 

50  34 

M 

72  51 

M 

99  00 

i^ 

35  58 

11  22 

30  49 

51  13 

73  36 

99  55 

37  35 

}& 

11  58 

y* 

31  26 

y* 

51  53 

y% 

74  21 

y-2 

100  51 

y* 

39  16 

12  34 

32  3 

52  33 

75  6 

101  48 

41  1 

5i 

13  10 

% 

32  40 

% 

53  13 

% 

75  51 

H 

102  45 

% 

42  51 

13  46 

33  17 

53  53 

76  36 

103  43 

44  46 

3 

14  22 

i 

33  54 

11 

54  34 

15 

77  22 

19 

104  41 

23 

46  48 

14'  58 

34  33 

55  14 

78  8 

105  40 

48  58 

i/ 

5  34 

y* 

35  10 

IX 

55  55 

i/ 

78  54 

M 

106  39 

y± 

51  17 

• 

6  10 

35  47 

56  35 

79  40 

107  40 

53  48 

\s 

6  46 

y* 

IX 

57  16 

L£ 

80  27 

y% 

108  41 

y* 

56  34 

7  22 

37  3 

57  57 

81  14 

409  43 

59  43 

a/ 

7  59 

H 

37  41 

H 

58  38 

% 

82  2 

ax 

110  46 

% 

63  27 

8  35 

38  19 

59  19 

82  49 

111  49 

168  18 

4 

19  12 

8 

38  57 

12 

60  00 

16 

83  37 

20     112  53 

24 

180  00 

19  48 

39  35 

60  41 

84  26 

113  58 

I 

(3)  With  the  same  table,  using  feet  instead  of  inches.  From 
any  point  measure  12  feet  toward  *  each  object,  and  place  marks.  Measure  the 
distance  in  feet  between  these  marks.  Suppose  the  first  column  in  the  table  tc 
be  feet  instead  of  inches.  Then  opposite  the  distance  in  feet  will  be  the  angle. 

Yz  foot  =  1.5  inches. 


1  in.   =  .083  ft. 

2  ins.  =  .167  ft. 

3  ins.  =  .25  ft. 


4  ins.  =  .333  ft. 

5  ins.  =  .416  ft. 

6  ins.  =  .5  ft. 


7  ins.  =  .583  ft. 

8  ins.  =  .667  ft. 

9  ins.  =  .75  ft. 


10  ins.  =    .833  ft. 

11  ins.  =    .917  ft. 

12  ins.  =  1.0  ft. 


(4)  Or,  measure  toward  *  each  object  100  or  any  other  number  of 
«>t,  and  place  marks.    Measure  the  distance  in  feet  between  the  marks.    Then 


Sine  of  half  _ 
the  angle 


half  the  distance  between  the  marks 


the  distance  measured  toward  one  of  the  objects 
*From  a  table  of  sines  tind  this  angle  and  multiply  it  by  2- 


159 

WEIGHT  OF  A  CUBIC  FOOT  OF  SUBSTANCES. 

Trautwine. 

Name  of  substances.  Average  weight,  Ibs. 

Aluminum, 162 

Brick,  best  pressed 

"      common,  hard 125 

soft 100 

Coal,  Pennsylvania  anthracite,  solid 93 

broken,  loose 54 

moderately  shaken 58 

heaped bushel. . . .  (77  to  83) 

Bituminous,  solid 84 

broken,  loose 49 

heaped,  loose bushel (74) 

Coke,  loose 23  to  32 

heaped  bushel 35  to  42 

Cement,  Amei  ican  Hydraulic,  Rosendale 56 

"         Louisville 50 

English             "          Portland 90 

Clay,  loose 63 

Earth,  common  loam,  dry,  loose 76 

'•      moderately  rammed 95 

"      as  soft  mud 108 

Flint 162 

Glass 157 

Gneiss 168 

Granite 170 

Gravel 90  to  106 

Ice :.  58.7 

Iron,  cast 450 

"       wrought 480 

Lead 711 

Lime,  loose  or  in  small  lumps 53 

S"       struck  bushel. . . .  [66] 

imestone  and  marble 168 

loose,  in  fragments 

Masonry  of  Granite  or  limestone,  well  dressed 

"  mortar  rubble 154 

"  sandstone,  well  dressed 144 

Mortar,   hardened 103 

Quartz 165 

Salt,  coarse 45 

"     fine 49 

Sand,  pure  quartz,  dry.  loose 90  to  106 

"      well  Shaken 99  to  117 

"      wet 118  to  130 

Sandstone 151 

Shales 162 

Silver 655 

Snow,  freshly  fallen 5  to  12 

"      moistened  and  compacted 15  to  50 

Steel 490 

Water,  pure.  62.425  [Fuller],  62. 37925  [HaswellJ   approximately  62^ 

sea 64.3 

WOODS 

Ash 47 

Boxwood 60 

Cherry 42 

Cork 16 

Elm 35 

Hemlock .* 25 

Hickory 53 

Maple 35 

Oak,  live ....  59,              white ....  48,           red  or  black ....  32  to  45 
Pine,  white  —  2o  yellow 35,  southern 45 

Green  timber  usually  weighs  from  £  to  £  more  than  dry. 


160 
TABLE  NO.  59. 

NAILS  AND  SPIKES. 


Carnegie,  Phipps  &  Co. 


Standard  Steel  Wire  Nails.          |  Steel  wire  spikes.  |Com'n.  iron  na'ls 


Size. 

Long 

Common. 

Finishing. 

Long 

Diam 
ins. 

No. 

perlb 

Size. 

Long 

No. 
perlb 

Diam 
ins. 

No  . 
perlb 

Diam 
ins. 

No. 
perlb 

2  d 

1  in. 

.0524 

1060 

.0453 

1558 

3  in. 

.1620 

41 

2  d 

1  in. 

800 

3  d 

u  • 

.0588 

640 

.0508 

913 

3A  " 

.1819 

30 

8  d 

U 

400 

4  d 

14  ' 

.0720 

380 

,0508 

761 

4  " 

.2043 

23 

4  d 

14 

300 

5  d 

If  ' 

.0764 

275 

.0571 

500 

44  " 

.2294 

17 

5  d 

U 

200 

6  d 

2  * 

.0808 

210 

.0641 

350  - 

5  " 

.2576 

13 

6  d 

2 

150 

7  d 

2i  * 

.0858 

160 

.0641!  315 

5*  " 

.2893 

11 

7  d 

2i 

120 

8  d 

24  ' 

.0935 

115 

.0720 

214 

6  " 

.2893 

10 

8  d 

& 

85 

9  d 

2f  ' 

.0963 

93 

.0720 

195 

64  " 

.2249 

7| 

9'  d 

21 

75 

10  d 

3  ' 

.1082 

77 

.0808 

137 

7  " 

.2249 

7 

10  d 

3 

60 

12  d 

3i  ' 

.1144 

60 

.0808 

127 

8  " 

.3648 

5 

12  d 

3J 

50 

16  d 

34  ' 

.1285 

48 

'.0907 

90 

9  " 

.3648 

44 

16  d 

34 

40 

20  d 

4  ' 

.1620 

31 

.1019 

62 

20  d 

4 

20 

30  d 

4}  • 

.1819 

22 

30  d 

44 

16 

40  d 

5  * 

.2043 

17 

=0  d 

5 

14 

50  d 

5*  * 

.2294 

13 

50  d 

54 

11 

60  d 

6  •' 

.2576 

11 

60  d 

6 

8 

TABLE  NO.  60. 

WEOUGHT  SPIKES. 


Number  to  a  keg  of  150  pounds. 


Carnegie,  Phipps  &  Co. 


Length 
Ins. 

iin. 
No. 

A  in. 
No. 

fin. 
No. 

Length 
Ins. 

i  in. 
No. 

*in< 
No. 

fin. 
No. 

A  in. 

No. 

4  in. 
No. 

3 

2250 

7 

1161 

622 

482 

445 

306 

34 
44 

1890 
1650 
1464 

i208 
1135 
1064 

8 
9 
10 

635 
573 

455 
424 

391 

384 
300 
270 

256 
240 
222 

5 

1380 

930 

742 

11 

249 

203 

6 

1292 

868 

570 

12 

236 

180 

TABLE  NO.  61. 
TABLE  OF  MANILLA  KOPE. 


Trautwine. 


Diam- 
eter 
Ins. 

Circum- 
ference 
Inches. 

Wt. 
per  ft 
Ibs. 

Breaking  load. 

Diam- 
eter 
[nches  . 

Cir- 
cumf. 
Ins. 

Wt. 
per  ft 
Ibs. 

Breaking  load. 

Tons. 

Lbs. 

Tons. 

Lbs. 

.239 
.318 
.477 
.636 
.795 
.955 
1.11 

? 

f 

34 

.019 
.033 
.074 
.132 
.206 
.297 
.404 

.25 
.35 
.70 
1.21 
1.91 
2.73 
3.81 

560 
784 
1  568 
2  733 
4  278 
6  115 
8  534 

1.27 
1.43 
1.59 
1.75 
1.91 
2.07 
2.23 

4 

g 

f 

64 

.528 
.668 
.825 
.998 
1.19 
1.39 
1.62 

5.16 
6.60 
8.20 
9.80 
11.4 
13.0 
14.6 

11  558 
14  784 
18  368 
21  952 
25  536 
29  120 
32  704 

TABLE  NO.  62. 

1  cubic  yard  =  201.95  gallons. 


161 


WELL  DIGGING. 

Adapted  from  Trautwine. 


Diameter 

Cubic  yds. 
for   each 

Diameter 

Cu.   yds. 
for   each 

Diameter 

Cubic  yards 
for  each 

in  feet. 

foot  of 

in  feet. 

foot  of 

in  feet. 

foot  in 

depth. 

depth  . 

depth. 

1 

.0291 

3* 

.3563 

6 

1.047 

| 

.0455 

.4091 

i 

1.136 

.0654 

4* 

.4654 

i 

1.229 

3 

.0891 

i 

.5254 

1.325 

2 

.1164 

.5890 

7 

1.425 

i 

.1473 

I 

.6563 

i 

1.636 

I 

.1818 

5 

.7272 

8 

1.862 

.2200 

i 

.8018 

i 

2.102 

3* 

.2618 

.8799 

9 

2.356 

i 

.3073 

1 

.9617 

* 

2.625 

For  diameters  twice  as  great  as  those  given  in  the  table, 
for  the  cu.  yds .  of  digging,  take  out  those  opposite  %  of  the 
greater diam., and X by  4.  Thus,  for  the  cu.  yds.  in  each  foot 
of  a  well  12  ft.  in  diam.,  take  out  the  yds.  for  a  well  of  6  ft. 
diam.  andxby  4....1.074x4=4.188=cu.  yds,  for  a  well  of  12 
feet  diameter. 

TABLE  NO.  63. 

CAPACITY  OF  CISTERNS  IN  GALLONS. 

For  each  10  niches  in  depth.  Haswell. 


Diam. 

Gallons  . 

Diam. 

Gallons  . 

Diam. 

Gallons. 

Diam. 

Gallons. 

Feet. 
2. 
2.5 
3. 
3.5 
4. 
4.5 

19.50 
30.60 
44.60 
59.97 
78.33 
99.14 

Feet. 
5. 
5.5 
6. 
6.5 
7. 
7.5 

122.40 
148.10 
176.25 

206.85 
239.88 
275.40 

Feet. 
8. 
8.5 
9. 
9.5 
10. 
11. 

313.33 
353.72 
396.56 
461.40 
.  489.60 
592.40 

Feet. 
12 
13 
14 
15 
20 
25 

705.0 
827.4 
959.6 
1101.6 
1958.4 
3059.9 

In  this  table  the  capacity  being  given  for  10  inches  it  is 
but  necessary  to  divide  by  10  by  moving  the  decimal  point 
one  place  to  the  left,  in  order  to  get  the  capacity  for  1  inch . 
Thus,  the  capacity  for  6  ft.  diam  and  10  inches  deep =176.25 
gals.,  and  for  1  inch  deep  it =17. 625  gals.  The  capacity  for 
any  depths  may  be  found  by  multiplying  the  capacity  for  1 
inch  by  the  depths  in  inches.  Example.  How  many  gals, 
in  a  cistern  12  feet  in  diam.  and  9  feet  deep?  9  ft. =108  m. 
70.5,  gals,  in  one  inch,  x  108= 7614  gals.  Ans. 
TABLE  NO.  64. 


CAPACITY  OF  CISTERNS  IN  BARRELS.  OF  31j  GALLONS.    Leffel. 
Depth  Diameter  in  feet. 


in    feet. 

5 

6 

7- 

8 

9 

10 

11 

12 

13 

14 

5 

23.  31  33.  6 

45.7 

59.7 

75.5 

93.2 

112.8 

134.3 

157.6 

182.8 

6 

28.0 

40.3 

54.8 

71.7 

90.6 

111.9 

135.4 

161.1 

189.1 

219.3 

7 

32.747.0 

64.0 

83.6 

105.7 

130.6 

158.0 

188.0 

220.6 

255.9 

8 

37.3:53.7 

73.1 

95.5 

120.9 

149.2 

180.5 

214.8 

252.1 

292.4 

9 

42.060.4 

82.2 

107.4 

136.0 

167.9 

203.1 

241.7 

283.7 

329.0 

10 

46.7 

67.1 

91.4 

119.4 

151.1 

186.5 

225.7 

268.6 

315.2 

365.5 

11 

51.373  9 

100.5 

131.3 

166.2 

205.1 

243.2 

295.4 

346.7 

402.1 

12 

56.0180.6 

109.7 

143.2 

181.3 

223.8 

270.8 

322.3 

378.2 

438.6 

13 

60.787.3 

118.8 

155.2 

196.4 

242.4 

293.4 

349.1 

409.7 

475.2 

14         65.394.0 

T27.9 

167.1 

211.5 

2H1.1 

315.9 

376.0 

441.3 

511.8 

162 
A BAKREL. 

The  standard  wine  barrel  contains  31^  gals,  of  231  cu.  in. 
In  Pennsylvania  a  wine  bbl. =32  gals.  The  standard  wine 
bbl.  contains  4.211  cu.  ft.  A  hogshead =63  gals.  The  aver- 
age size  of  the  barrel  used  for  oil  or  vinegar  is  about  19J^ 
ins.  diam.  of  head,  22%  ins.  diam.  of  bung,  and  29  to  30  ins. 
long  and  contains  from  48  to  52  gals,  the  contents  being 
usually  marked  on  the  head. 

In  figuring  on  the  barrel  capacity  of  a  cistern  the  size  or 
volume  of  the  barrel  should  be  given  or,  in  case  of  contract 
work,  it  should  be  specified.  By  reason  of  the  size  of  the 
ordinary  barrel  being  from  48  to  52  gals,  it  would,  for  con- 
venience, be  best  to  figure  on  the  basis  of  50  gals,  to  the  bbl. 
The  bbl.  of  31^  gals.,  however,  is  the  one  commonly  used. 

MISCELLANEOUS. 
Shingles.    1000  laid  4  inches  to  the  weather  will  cover  one 

square  of  100  sq.  ft.  and  5  Dbs  of  nails  will  lay  them. 
Lath.    1000  will  cover  70  sq.  yds.  of  surface  and  11  flbs.  of 

nails  will  lay  them. 
Mortar.    8  bushels  of  lime,  16  of  sand  and  1  of  hair  will 

make  mortar  for  100  sq.  yds,  of  surface. 
Stone  Wall.    1  cord  of   stone,  3  bushels  of  lime,  and  1  cu. 

yd.  of  sand  will  lay  100  cu.  ft.  of  wall. 
Brick.    5  courses  of  brick  will  lay  1  foot  high. 

6  brick  in  a  course  will  lay  a  flue   4  by  12  inches. 


7 


9 
10 

Thickness  of  wall. 


12 

8  •'  16  ' 
12  "  12  ' 
12  •'  16  ' 
12  "  20 

No.  to  sq.  ft.  of  wall. 


8  inches  =  1     brick 14 

12  li         '     21        (No  allowance  being  made  for 

16      "  2          4     28        <  mortar  or  extra  thickness  of 

20      "  2i  35        (brick.    Brick  8  X  4  X  2  inches. 

24      "  3          *     42 

Flooring  &  Siding.  Add  £  to  the  area  to  be  covered  to  allow 
for  lap.  This  is  the  lumberman's  rule  in  selling. 

Hay.  Get  the  number  of  cubic  feet  in  the  mow  or  stack; 
then,  for  new  hay,  divide  by  about  270  to  get  tons;  for 
old  hay,  divide  by  about  230  to  get  tons;  and  for  dry 
clover  divide  by  about  310  to  get  tons.  The  weights  of 
different  grasses,  in  the  different  stages  of  dryness  or 
compression,  vary  so  greatly  that  any  rule  for  weight  by 
volume  must  be  so  purely  arbitrary  as  to  be  of  but 
little  value. 

Corn.    Get  the  cubic  feet  and  divide  by  2J£  to  get  bushels. 

Apples,  Potatoes,  &  Grain  in  Bin.  Get  cu.  ft.  and X  by  8, 
then  point  off  1  place  for  decimals  to  get  contents  in 
bushels— or— from  cubic  ft.  deduct  £  and  the  remainder 
=bushels  in  bin.  (bush. =1.24445  cu.  ft.)  Example. — 
100  cu.  ftx8=800,  pointed  off=80  bush—  or— 100— £  (20) 
=80  bushels. 


163 

LUMBER  TABLES. 

TABLE  NO.  65. 

FEET,  BOARD  MEASURE,  IN    JOIST,    SCANTLING  AND   TIMBER. 


Length 
in  feet. 

IO 

12 

14 

16 

18 

20 

22      24 

26 

28 

30 

Size  in 
Inches. 

FEET,  BOARD  MEASURE. 

2x4 

HH      s     9:\     101 

12 

13£ 

14s 

16 

174 

181 

20 

10 

12 

14         16 

18 

20 

.22 

24 

26 

28 

30 

2  x    8 

134 

16 

193       214 

24 

261 

294 

32 

34| 

374 

40 

2x|Q 

161 

20 

23^ 

26g 

30 

334 

361 

40 

434 

46| 

50 

2x|2 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

2x|4 

2N 

'28 

32| 

37i 

42 

461 

514 

56 

631 

654 

70 

3x4 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

3x6 

15 

18 

21 

24 

27 

30 

33 

36 

39 

42 

45 

§x    8 

20 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

1  O 

25 

30 

35 

40 

45 

50 

55 

60 

65 

70 

75 

3x|2 

so       36 

42 

48 

54 

60 

66 

72 

78 

84 

90 

3x|4 

:tt        t2 

49 

56 

63 

70 

77 

84 

91 

98 

105 

4        4 

in  A       IB 

18| 

214 

24 

261 

294 

32 

341 

374 

40 

4x6 

3)          21 

28         32 

36 

40 

44 

48 

52 

56 

60 

4x    § 

26?        32 

371       421 

48 

534 

58§ 

64 

694 

741 

80 

4  x  IO 

33| 

40 

46§       53' 

60 

661 

734 

80 

861 

934 

100 

4XI  2 

40 

48 

56 

64 

72 

80 

88 

96 

104 

112 

120 

6  x    6 

30 

36 

42 

48 

54 

60 

66 

72 

78 

84 

90 

6x8 

40 

48 

56 

64 

72 

80 

88 

96 

104 

112 

120 

6x|Q 

60 

60 

70 

80 

90 

100 

110 

120 

130 

140 

150 

6x12 

HO 

72 

84 

96 

108 

120 

132 

144 

156 

168 

180 

§x    8 
x  IO 

53} 

B6J 

64 

80 

741 
93i 

85i 
1061 

96 
120 

106§ 
1334 

1174 
146| 

128 
160 

1381 
1734 

1494 
186§ 

160 
200 

8x12 

80        96 

112 

128 

144 

160 

176 

192 

20? 

224 

240 

I  Ox  IO 

8.34 

100 

117 

133 

150 

167 

183 

200 

217 

233 

250 

IOx|  2 

100 

120 

140 

160 

180 

200 

220 

240 

260 

280 

300 

1  2x|  2 

120 

144 

168 

192 

216 

240 

264 

288 

312 

336 

360 

12x14 

140 

168 

196 

224 

252 

280 

308 

336 

364 

392 

420 

14x14 

1634 

196 

228| 

261i 

294 

3261 

3594 

392 

424§ 

4574 

490 

TABLE  1X0.  66. 


FEET—  BOARD  MEASURE,  IN  1  INCH  BOARDS.            New  ' 

Width 
in 
inches. 

Length  in  feet. 

8 

10 

12 

14 

16 

18 

20 

22 

24 

4 

6 
8 
10 
12 
14 
16 
18 
20 

2% 
4 

6% 

8 

12/3 

5  3 

6% 

10  3 

11% 
15  3 

4 
6 
8 
10 
12 
14 
16 
18 
20 

11>* 
14  3 

18% 
21 
23^ 

8  3 

13^ 
16  3 

21^ 
24  ° 
26% 

6 
9 
12 
15 
18 
21 
24 
27 
30 

€ 
P 

23^ 

s* 

33^ 

•I* 

111 

22 

25% 
29^ 
33 
36% 

8 
12 
16 
20 
24 
28 
32 
36 
40 

RULE  for  estimating  ft.  b.  m.  in  any  piece  of  board  or  timber.— [A  foot 
b.  m.  =  12  X  12  inches  by  1  inch  thick,  =  144  cubic  inches.]  Multiply  the 
width  by  the  thickness  •+•  product  by  12  and  X  quotient  by  length.  Thus : 

A  stick  8  by  10  inches   by  10  feet  equals  8  X  10  =  80  inches  of  sectional 

area  which  -*-  12  =6%  ft.  b.  m.  per  foot  of  length ;  this  X  10  =  66%  ft. 

3"  by  12"  by  10  equals  3  X  12  =  36  ,    36  -4-  12  =  3,    3  X  10  =  30  ft.  B.M. 

4"  by  6'  by  10'  equals  4  X  6  =  24,    24  -H  12  =  2,    2  X  10  =  20  ft.  B.M.&c. 


164 


From  Trail ti 


TABLE  NO.  67. 
ie's  ••t'ivil  Engineer's  Pocket  Book.-' 


of  a  Degree  of  I><m-  im<h-  in  different  Latitudes, 

ami  at  the  level  Of  the  Sea.  These  lengths  are  in  common  land  or  statute  miles, 
of  5280  ft.  Since  the  figure  of  the  earth  hns  never  been  precisely  ascertained,  these  are  but  close  ap 
proximatious.  Intermediate  ones  maybe  found  correctly  by  simple  proportion.  i°  of  longitude 
corresponds  to  4  mine  of  civil  or  cluck  time;  1  min  of  longi'tude  to  4  sees  of  time. 


tft?'!  Miies- 

Degof 
Lat. 

Miles. 

Degof 

Miles. 

Degof, 
Lat.   ! 

Miles. 

Degof 
Lat. 

Miles. 

Degof 
Lat. 

Miles. 

0          69.16 

14 

67.12 

28 

61.11 

42 

51.47 

56 

38.76 

70 

23.72 

2     !     69.12 

16 

66.50 

30. 

59.94 

44 

49.83 

58 

36.74 

72 

21.43 

4 

68.99 

18 

65.80 

32 

58.70 

46 

48.12 

60 

34.67 

74 

19.12 

6 

68.78 

20 

65.02 

34 

57.39 

48 

46.36 

62 

32.55 

76 

16.78 

8 

68.49 

22 

64.15 

36 

56.01 

50 

44.54 

64 

30.40 

78 

14.42 

10 

68.12 

24 

63.21 

38 

54.56 

52 

42.67 

66 

28.21 

80 

12.05 

12 

67.66 

26 

62.20 

40 

53.05 

54 

40.74 

68 

25.98 

82 

9.66 

Inches  reduced  to  Decimals  of  a  Foot.        NO  errors. 

Ins. 

Foot. 

Ins. 

Foot. 

Ins. 

Foot. 

Ins. 

Foot. 

Ins. 

Foot. 

Ins. 

Foot. 

0 

.0000 

2 

.1657 

4 

.3.53  5 

6 

.5000 

8 

.66C7 

10 

.8333 

1-32 

.0026 

.16J3 

.3,)5i> 

.5026 

.6693 

.8359 

1-16 

.0052 

.1719 

.33*5 

.5052 

.6719 

.8385 

3-32 

.0078 

.1745 

.3*11 

.5078 

.6745 

.8411 

% 

.0104 

H 

.1771 

X 

.8438 

M 

.5104 

h 

.6771 

H 

.8438 

5-33 

.0130 

.1797 

.3164 

.5130 

.€797 

.8464 

:-;-!« 

.0156 

.1823 

.3  WO 

.5150 

.6823 

.8490 

7-32 

.0182 

.1849 

.3516 

.5182 

.6849 

.8516 

K 

.0208 

% 

.1875 

% 

.3542 

y± 

.5'208 

y* 

.6875 

% 

.8542 

9-32 

.0234 

.1931 

.3568 

.5234 

.6901 

.8568 

5-16 

.0260 

.1927 

.3594 

.5260 

.6927 

.8594 

11-82 

.0286 

.1955 

.3620 

.52b6 

,  .6953 

.8620 

% 

.0313 

% 

.197J 

38 

.364(5 

% 

.5313 

% 

.6979 

% 

.8646 

13-32 

.0339 

.2005 

.3672 

.5339 

.7005 

.8672 

7-16 

.0365 

.2031 

.3698 

.5365 

.7031 

.8698 

15-32 

.0391 

.2057 

.3724 

.5391 

.7057 

.8724 

\i 

.0417 

X 

.20t  j 

1;, 

.3750 

« 

.5417 

y* 

.7083 

y* 

.8750 

17-32 

.0443 

.2109 

.3776 

.5443 

.7109 

.8776 

9-16 

.0469 

.2135 

.3802 

.5469 

.7135 

.8802 

19-32 

.0495 

.2161 

.3828 

.5495 

.7161 

.8828 

K 

.0521 

K 

.2188 

H 

.3854 

N 

.5521 

% 

.7188 

% 

.8854 

21-32 

.0547 

.221  1 

.3880 

.5547 

.7214 

.8880 

11-16 

.0573 

.2240 

.3906 

.5573 

.7240 

.8906 

23-32 

.059J 

.2263 

.3932 

.5599 

.7266 

.8932 

K 

.0625 

« 

.2231 

H 

.3958 

34 

.5625 

*A 

.7292 

N 

.8958 

25-32 

.0651 

.2318 

.3984 

.5651 

.7318 

.8984 

13-16 

.0677 

.2344 

.4010 

.5677 

.7344 

.9010 

27-32 

.070.5 

.2370 

.4036 

.5703 

.7370 

.9036 

% 

.0729 

% 

.2396 

H 

.4063 

h 

.5729 

% 

.73% 

X 

.9063 

29:3 

.0755 

.2422 

.4089 

.5755 

.7422 

.9089 

15  IB 

.0781 

.2448 

.4115 

.5781 

.744fc 

.9115 

31-32 

.0807 

.2474 

.4141 

.5807 

.7474 

.9141 

1 

.0833 

3 

.2500 

5 

.4167 

7 

.5833 

9 

.7500 

11 

.9167 

1-32 

.0859 

.252(5 

.4193 

.5859 

.7526 

.9193 

1-16 

.0885 

.2552 

.4219 

.58*5 

.7552 

.9219 

3-3U 

.0911 

.2578 

.4245 

.5911 

.7578 

.9245 

K 

.0938 

% 

.2604 

U 

.4271 

h 

.59S8 

M 

.7604 

X 

.9271 

5-32 

.0964 

.2630 

.4297 

.5964 

.7630 

.9297 

3-  16 

.0990 

.2656 

.4323 

.5l$)0 

.7656 

.9323 

7-32 

.1016. 

.2882 

.4349 

.6016 

.7682 

.9349 

•y< 

.1042 

tt 

.2708 

X 

.4375 

i/ 

.6042 

y± 

.7708 

K 

.9375 

9-32 

.1068 

.2734 

.4401 

' 

.6068 

.7734 

.9401 

5-16 

.1094 

.2760 

.4427 

.6094 

.7760 

.9427 

11-32 

.1120 

.2786 

.4453 

.6120 

.7786 

.9453 

h 

.1146 

% 

.2813 

% 

.4479 

% 

.6146 

% 

.7813 

% 

.9479 

l.€l-32 

.1172 

.2&?9 

.4505 

.6172 

.7839 

.9505 

1  -16 

.1198 

.2865 

.4531 

.6198 

.7865 

.9531 

15-S2 

.1224 

.2891 

.4557 

.6224 

.7891 

.9557 

H 

.1250 

1A  i     .2917 

y* 

.4583 

x. 

.6250 

X 

.7917 

M 

.9583 

n-sz 

.1276 

.2943 

.4609 

.6276 

.7943 

.9609 

9-16 

.1302 

.2969 

.4635 

.6302 

.7969 

.9635 

19-32 

.1328 

.2995 

.4661 

.6328 

.7995 

.9661 

fc 

.1354 

% 

.3021 

% 

.4688 

% 

.6354 

% 

.8021 

% 

.9688 

21  -32 

.1380 

.3047 

.4714 

.6380 

.8047 

.9714 

11-16 

.1406 

.3073 

.4740 

.6406 

.8073 

.9740 

23-32 

.1432 

.3099 

.4766 

.6432 

.8099 

.9766 

H 

.1458 

H 

.3125 

% 

.4792 

H 

.6458 

% 

.8125 

H 

.9792 

25-32 

.1484 

.3151 

.4818 

.6484 

.8151 

.9818 

13-16 

.1510 

.3177 

.4844 

.6510 

.8177 

.9*44 

27-32 

.1536 

.3203 

.4870 

.6536 

.8203 

.9870 

H 

.1563 

% 

.3229 

% 

.4896 

% 

.6563 

% 

.8229 

% 

.9HH5 

W32 

.1589 

1     .3255 

.4922 

.6589 

.8255 

.9922 

15-16 

.1615 

.3281 

.4948 

.6615 

.8281 

.9948 

81-32 

.1641 

I      .3307 

.4974 

.6641 

.8307 

.9974 

165 


TABLE  NO.  68. 

DECIMALS  OF  AN  INCH  FOR  EACH  &th.  INCH. 


^ds. 

Aths. 

Decimal. 

Fraction. 

&ds. 

Aths. 

Decimal. 

Fraction. 

1 

2 

1 
2 
3 
4 

.015625 
.03125 
.046875 
.0625 

1-16 

17 

18 

33 
34 
35 
36 

.515625 
.53125 
.546875 
.5625 

9-16 

3 

5 
6 

.078125 
09375  . 

19 

37 

38 

.578125 
.59375 

4 

7 
8 

'.109375 
.125 

1-8 

20 

39 
40 

.609375 
.625 

5-8 

9 

.  140625 

41 

.640625 

5 

10 

'.  15625 

21 

42 

.65625 

11 

171875 

43 

.671875 

6 

12 

.1875 

3-16 

22 

44 

.6875 

11-16 

13 

203125 

45 

.703125 

7 

14 

21875 

23 

46 

.71875 

15 

.234375 

47 

.734375 

8 

16 

.25 

1-4 

24 

48 

.75 

3-4 

17 

.  265625 

49 

.765625 

9 

18 

.  28125 

25 

50 

.78120 

19 

296875 

51 

.796875 

10 

20 

.3125 

5-16 

26 

52 

.8125 

13-16 

21 

.328125 

53 

.828125 

11 

22 

.  34375 

27 

54 

.84375 

23 

.359375 

55 

.859375 

12 

24 

.375 

3-8 

28 

56 

.875 

7-8 

25 

.390625 

57 

.890625 

13 

26 

.40625 

29 

58 

.90625 

27 

.421875 

59 

.921875 

14 

28 

.4375 

7-16 

30 

60 

.9375 

15-16 

29 

.453125 

61 

.953125 

15 

30 

.46875 

31 

62 

.96875 

31 

.484375 

63 

.984375 

16 

32 

.5 

1-2 

32 

64 

1  . 

1 

166 


TABLE  NO.  69. 


From  Traiitwine's  "Civil  Engineer**  Pocket  Book/' 

HYDRAULICS. 


TABLE          Of  the 

hers.     In  this  table  the  i 
mansions  ;  that  is,  both  iu  iuche: 


square  roots  of  the  fifth  powers  of  iium- 

i umbers  and  the  roots  are  supposed  to  be  in  the  same  di- 


j  feet,  <tec.     See  the  i: 


Sq.  Rt. 

Sq.  Rt. 

Sq.  Rt. 

Sq.  Kt. 

Sq.  Rt. 

Sq.  Rt. 

Power. 

Power. 

Power. 

Power. 

Power. 

Power. 

.25 

.o;u 

7. 

129.64 

17.5 

1281.1 

51. 

5351 

49 

16807 

76 

50354 

.5 

.177 

7.25 

141.53 

18. 

1374  6 

31.5 

5569 

50 

17678 

77 

52027 

.75 

.485 

7.5 

154.05 

18.5 

1472.1 

32. 

5793 

5.1 

18575 

78 

53732 

1. 

1. 

7.75 

167.21 

19. 

1573.6 

32.5 

6022 

52 

19499 

79 

55471 

1.25 

1.747 

8. 

181.02 

19.5 

1679.1 

33. 

6256 

53 

20450 

80 

57243 

1.5 

2.756 

8.25 

195.50 

20. 

1788.9 

33.5 

649<> 

54 

21428 

81 

59049 

1.75 

4.051 

8.5 

210.64 

20.5 

1902.8 

34. 

6741 

55 

22434 

82 

60888 

2. 

5.657 

8.75 

226.48 

21. 

2020.9 

34.5 

6991 

58 

28468 

83 

62762 

2,25 

7.594 

9. 

243. 

21.5 

2143.4 

35. 

7247 

57 

24529 

84 

64669 

2.5 

9.882 

9.25 

260.23 

22. 

2270.2 

35.5 

7509 

58 

25620 

85* 

66611 

2.75 

12.541 

9.5 

278.17 

22.5 

2401.4 

36. 

77*i 

59 

26738 

86 

63533 

& 

15.588 

9.75 

296.83 

23. 

2537. 

36.5 

8049 

60 

.    27886 

87 

70599 

3.25 

19.042 

10. 

316.23 

23.5 

2677.1 

37. 

8327 

61 

29062 

88 

72646 

3.5 

22.918 

10.5 

357.2 

24. 

2821.8 

37.5 

8611 

62 

30268 

89 

74727 

3.75 

27.232 

11. 

401.3 

24.5 

2971.1 

38. 

8901 

63 

31503 

90 

76843 

4. 

32. 

11.5 

448.5 

3125. 

38.5 

9197 

64 

32768 

91 

78996 

4.25 

37.24 

12. 

498.8 

2o!5 

3283.6 

39._ 

9498 

65 

34063 

92 

81184 

4.5 

42.96 

12.5 

552.4 

26. 

3446.9 

9806 

66 

35388 

93 

83408 

4,75 

49.17 

13. 

609.3 

26.5 

3615.1 

40'. 

10119 

67 

36744 

94 

85668 

5. 

55.90 

13.5 

669.6 

27. 

3788. 

41. 

10764 

68 

38131 

95 

87965 

5.25 

63.15 

14. 

733.4 

27.5 

3965.8 

42. 

11432 

69 

39548 

96 

90298 

5.5 

70.94 

14.5 

800.6 

28. 

4148.5 

43. 

12125 

70 

40996 

97 

92664 

5.75 

79.28 

15. 

871.4 

28.5 

4336.2 

44. 

12842 

71 

42476 

98 

95075 

6. 

88.18 

15.5 

945.9 

29. 

4528.9 

45. 

13584 

72 

43988 

99 

97519 

6.25 

97.66 

16. 

1024. 

29.5 

4726.7 

46. 

14351 

73 

45531 

100 

100000 

6.5 

107.72 

16.5 

1105.9 

30. 

4929.5 

47. 

15144 

74 

47106 

6.75 

118.38 

17. 

1191.6 

30.5 

5138. 

48. 

15%3 

75 

48714 

Numbers,  in  inches.     Square  roots  of  fifth  powers,  in  feet. 


Sq.  Rt.  of 
5th  Pow. 

Sq.  Rt.  of 
5th  Pow. 

Sq.  Rt.  of 
5th  Pow. 

Ins. 

Feet. 

Ins. 

Feet. 

Ins. 

Feet. 

i^ 

.00006 

39* 

.0547 

12. 

1.000 

H     j      -00017 

4. 

.0641 

% 

1.108 

M 

.00035 

•Lt 

.0731 

13. 

1.221 

M 

.00062 

% 

.0827 

i^ 

1.342 

.00098 

H 

.0971 

14. 

1.470 

r/ 

.00144 

5. 

.1120 

y^ 

1.605 

j^ 

.0020 

1^ 

.1271 

15. 

1.747 

H 

.0027 

Ht 

.1428 

1.896 

.0035 

.1590 

16. 

2.053 

u 

.0044 

6. 

.1768 

HI 

2.217 

1£ 

.0055 

/4 

.2160 

17. 

2.389 

N 

.0067 

7. 

.2599 

M 

2.567 

K 

.0081 

.3088 

18. 

2.756 

J^ 

.0096 

8. 

.3628 

2.950 

2. 

.0113 

.4228 

19. 

3.155 

.0152 

9. 

.4871 

3.365 

iz 

.0198 

j^ 

.5577 

20. 

3.586 

•9 

.0252 

10. 

.6339 

^ 

3.813 

8. 

.0312 

.7162 

21. 

4.051 

.0383 

11. 

.8043 

H 

4.297 

§ 

H 

.8990 

22. 

4.551 

Sq.  Rt.  of 
5th  Pow. 

Sq.  Rt.  of 
5th  Pow. 

Ins. 

Feet. 

Ins. 

Feet. 

22  X 

4.813 

42 

22.92 

23 

5.086 

43 

24.31 

H 

5.365 

44 

25.74 

24 

5.657 

45 

27.23 

25 

6.264 

46 

28.77 

26 

6.909 

47 

30.36 

27 

7.593 

48 

32.00 

28 

8.316 

49 

33.69 

29 

9.079 

50 

35.44 

30 

9.882 

51 

37.25 

31 

10.73 

52 

39.13 

32 

11.61 

53 

41.02 

33 

12.54 

54 

42.96 

34 

13.51 

55 

44.97 

35 

14.53 

56 

47.05 

36 

15.59 

57 

49.17 

37 

16.69 

58 

51.35 

38 

17.84 

59 

53.60 

39 

19.04 

60 

55.90 

40 

20.29 

61 

58.2T 

41 

21.58 

TABLE  NO.  70.  167 

From  Trautuiiie'K  "Civil  Eii£-iiic>er's  Pocket  Book." 

MENSURATION. 


To  find  the  length  of  a  circular  arc  by  tbe  following1  table* 

Knowing  the  rad  of  the  circle,  and  the  measure  of  the  arc  in  deg,  min,  &c. 

RULE.  Add  together  the  lengths  in  the  table  found  respectively  opposite  to  the  deg,  min,  &c,  of 
tbe  arc.    Mult  the  sum  by  the  rad  of  the  circle. 

Ex.  In  a  circle  of  12.43  feet  rad,  is  an  arc  of  13  deg,  27  min,  8  sec.     How  long  is  the  arc? 
Here,  opposite  13  deg  in  the  table,  we  find,  .2268928 
27  min  "  "        "      .0078540 

*  sec    "  " 


Sum  rr  .2347856 
And  .2347856  X  12.43  or  rad  =  2.918385  feet,  the  reqd  length  of  arc. 

LENGTHS  OF  CIRCULAR  ARCS  TO  RAD  1. 


No  errors. 


Deg. 

Length. 

Deg. 

Length. 

Deg. 

Length. 

m.. 

Length. 

Sec. 

Length. 

1 

.0174533 

m 

1.0646508 

121 

2.1118484 

1 

.0002909 

1 

.0000048 

: 

.034906* 

62 

1.0821041 

122 

2.1293017 

2 

.0005818 

2 

.0000097 

3 

.0523599 

63 

1.0995574 

123 

2.  1407  550 

3 

.0008727 

3 

.0000145 

4 

.0698132 

64 

1.1170107 

124 

2.1642083 

4 

.0011636 

4 

.0000194 

5 

.0872665 

65 

1.1344640 

125 

2.1816616 

5 

.0014544 

5 

.0000242 

6 

.104719* 

66 

1.1519173 

126 

2.1991149 

6 

.0017453 

6 

.0000291 

7 

.1221730 

67 

1.1631)706 

127 

2.2165682 

7 

.0020362 

7 

.0000339 

8 

.1396263 

68 

1.1  868239 

128 

2.2340214 

8 

.0023271 

8 

.0000388 

9 

.1570796 

69 

1.2042772 

129 

2.2514747 

9  . 

.0026180 

9 

.0000436 

10 

.1745329 

70 

1.2217305 

130 

2.2689280 

10 

.0029089 

10 

.0000485 

11 

.1919862 

71 

1.2391*3* 

131 

2.2863813 

11 

.0031998 

11 

.0000533 

12 

.2094395 

72 

1.  2566:571 

132 

2.303H346 

12 

.0034907 

12 

.0000582 

13 

.22O92* 

73 

1.2740904 

133 

2.3212879 

13 

.0037815 

13 

.0000630 

14 

.2443461 

74 

1.2915436 

134 

2.3387412 

14 

.0040724 

14 

.0000679 

15 

.261799+ 

75 

1.8089W9 

135 

2.3561945 

15 

.0043633 

15 

.0000727 

16 

.2792527 

76 

1.3264502 

136 

2.3736478 

16 

.0046542 

16 

.0000776 

17 

.2967060 

77 

1.3439035 

137 

2..:911011 

17 

.0049451 

17 

.0000824 

18 

.3141593 

78 

1.36135G8 

138 

2.40S3544 

18 

.0052360 

18 

.0000873 

19 

.3316126 

79 

1.37^101 

139 

2.42*10077 

19 

.0055269 

19 

.0000921 

20 

.3490659 

SO 

1.3952634 

140 

2.4434610 

20 

.0058178 

20 

.0000970 

21 
22 

.3665191 
.3839724 

gj 

1.4137167 
1.43117D 

142 

2.47r3675 

"2 

!0063995 

22 

.0001018 
.0001067 

23 

.40142.17 

83 

1.4483233 

14:5 

2.4958208 

23 

.0066904 

23 

.0001115 

24 

.4188791) 

84 

1.4660766 

144 

2.)132741 

24 

.0069813 

24 

.0001164 

25 

.43633  .'3 

85 

1.4835299 

145 

2.5307274 

25 

.0072722 

25 

.0001212 

26 

.4537856 

86 

1.5009832 

146 

2.5481807 

26 

.0075631 

26 

.0001261 

27 

.4712389 

87 

1.51  84  >ii  4 

147 

2.5656340 

27 

.0078540 

27 

.0001309 

28 

.4886922 

88 

1.5358  3:)7 

148 

2.5830873 

28 

.0081449 

28 

.0001357 

29 

.5061455 

89 

1.553343) 

149 

2.6005406 

29 

.0084358 

29 

.0001406 

30 

.52359*8 

90 

1.57)7975 

150 

2.6179£:,9 

30 

.0087266 

30 

.0001454 

31 

.5410521 

91 

1.588219. 

151 

2.6354472 

31 

.0090175 

31 

.0001503 

32 

.55*5054 

92 

1.  6057*2  J 

152 

2.6529005 

32 

.009301-4 

32 

.0001551 

33 

.5759587 

93 

1.6231562 

JM 

2.6703538 

33 

.0095963 

33 

.0001600 

34 

.5934119 

94 

1.6406395 

154 

2.6878070 

34 

.0098902 

34 

.0001648 

35 

.6108652 

95 

1.65306'JS 

155 

2.705-J6C3 

35 

.0101811 

35 

.0001697 

36 

.6283185 

96 

1.6755161 

156 

2.  72271  M6 

36 

.0104720 

36 

.0001745 

37 

.6457718 

97 

1.69J5K594 

157 

2.7401f>(;9 

37 

.0107629 

37 

.0001794 

38 

.6632251 

98 

1.7104227 

158 

2.7576202 

S8 

.0110538 

38 

.0001842 

39 

.680678: 

99 

1.7278760 

159 

2.7750735 

:^9 

.0113446 

39 

.0001891 

40 

.6981317 

100 

1.7453293 

Ifr) 

2.7925268 

40 

.01163:  5 

40 

.0001939 

41 

.715585) 

101 

1.7827825 

161 

2.8099801 

1 

.0116264 

1 

.0001988 

42 

.7330383 

102 

1.7802358 

162 

2.P274334 

2 

.0122173 

2 

.0002036 

43 

.7504916 

103 

1.797999] 

163 

2.8448887 

3 

.0125082 

3 

.0002085 

44 

.7679449 

114 

1.8151424 

164 

2.SJVJ3IOO 

4 

.0127991 

4 

.0002133 

45 

.7853982 

1)5 

1.8:»2.-)<Ti7 

Ifi5 

2  t7f»7J'M3 

5 

.0130900 

5 

.0002182 

46 

.8023515  • 

106 

'  lAVKH't* 

u;6 

2>972ififi 

6 

.0133809 

6 

.0002230 

47 

.8293017 

107 

1  «"(7V''j'> 

167 

2.5H  16999 

47 

.0136717 

7 

.0002279 

48 

.83775:) 

i08 

l.-M'r-  ; 

168 

2.^2:',3l 

48 

.n!T9fi26 

8 

.0002327 

^9 

.8552113 

109 

1.9:)240S9 

1«9 

2.:-l4°(>Of,4 

49 

.0142535 

9 

.0002376 

50 

.87268  46 

no 

1.919*622 

170 

2.«W705!»7 

50 

.0145444 

50 

.0002424 

51 

.8901179 

111 

1.93731:5 

171 

2.9*45130 

:.l 

.014*353 

51 

.0002473 

52 

.90757-2 

112 

1.95476fc8 

172 

3.0019663 

52 

.0151262 

52 

.0002521 

53 

.9_>:W2t5 

1!3 

1.972*221 

173 

3.0194196 

53 

.0154171 

53 

.0002570 

54 

.912477^ 

1  '4 

1.9#K?-«S 

174 

3.0368729 

54 

.01570*0 

54 

.0002618 

55 

.95991  M 

115 

2.017'1"^ 

175 

3.054326? 

55 

.0159989 

55 

.0002666 

56 

.5*77  '-H 

1  '6 

2.  '"''2  1  5s  '9 

176 

3.07177H5 

=>6 

.0162897 

56 

.0002715 

57 

.994*377 

117 

2.0T2V-CV2 

177 

3.0Mt'_>2'.>s 

57 

Olfi5806 

57 

.0002763 

58 

1.0122910 

i  :s 

•AO.VHS.--! 

17« 

S.l'V.f.MU 

M 

.0168715 

58 

.0002812 

59 

1.0297443 

119 

,   2.07<W:s 

179 

S.W1394 

r>9 

.0171624 

59 

.0002860 

60 

1.  U47  15»7»; 

120 

1  2.0943951 

80 

.0174533 

60 

.0002909 

168 

EXPLANATION    OF  TABLES  OF  CIRCLES. 
It  will  be  noticed  that  there  are  three  tables  of  circles. 

FIRST        —Table  giving  diameters  in  units  and  EIGHTHS- 
SECOND  -  "        "        «     TENTHS 

THIRD  •'     TWELFTHS- 

The  diameter  in  all  cases  extending  to  100. 
The  following  rules  with  reference  to  the  table  giving  the 
diameters  in  TENTHS  will  also  be  of  value. 

To  compute  the  area  or  circumference  of  a  diameter  great- 
er than  100  and  less  than  1001: 

Kule— Take  out  the  area  or  circumference  from  the  table 
as  though  the  number  had  one  decimal,  and  move  the  deci- 
mal point  two  places  to  the  right  for  area  and  one  place 
for  the  circumference. 

Example— Wanted  the  area  and  circumference  of  567.  The 
tabular  area  for  56.7  is  2524.9687,  and  circumference  178.1283. 
Therefore  area  for  567=252496.87  and  circumf.=  1781. 283. 

To  comptue  the  area  or  circumference  of  a  diameter 
greater  than  1000. 

Rule— Divide  by  a  factor  2,  3,  4,  5,  etc . ,  if  practicable,  that 
will  leave  a  quotient  to  be  found  in  the  table;  then  multi- 
ply the  tabular  area  of  the  quotient  by  the  square  of  the 
factor,  to  get  required  area;  and  the  tabular  circumference 
by  the  factor  to  get  the  required  circumference. 

Example— Wanted  the  area  and  circumference  of  2109. 
Dividing  by  3  the  quotient  is  703,  for  which  the  area  is 
388,150.84  and  the  circumference  2208.54.  Therefore  area 
of  2109  =  388150.84  X  9  (  9  =  square  of  3  )  =  3493357.56,  and 
the  circumference  =  22  08.54  X  3  =  6625.62. 

The  following  rules  with  reference  to  table  giving  the 
diameters  in  EIGHTHS  will  also  be  found  of  value. 

If  the  required  diameter  is  not  in  the  table,  separate  it 
and  take  the  circumference  of  each  and  add  them. 

Example— Wanted  the  circumference  of  25f£  inches. 
Circumference  of  25  m.=78.5398  and  of  |J=2.06167;  adding 
these  we  get  80.60147  the  required  circumference.  This  pro- 
cess will  not  answer  for  the  area,  however.  In  case  the 
area  is  wanted,  reduce  the  given  diameter  to  a  decimal  and 
multiply  this  by  itself  and  the  product  by  .7854  (area=square 
of  diameter x. 7854).  Reduce  to  a  decimal  of  a  foot  or  of  an 
inch  by  use  of  tables  67  and  68.  See  AKEA  P.  152. 

Where  the  diameter  contains  more  than  one  decimal,  or 
where  it  contains  fractions  of  an  inch,  see  small  tables 
following  the  tables  giving  diameters  in  TENTHS  & 
TWELFTHS  respectively,  on  pages  177  and  184. 

See  rules  on  page  152  for  calculating  diameters,  circum- 
ferences, or  areas,  or  the  sides  of  equal  squares,  without  the 
use  of  tables. 


TABLE  NO.  71.  169 

From  Trautwine*s  ••fivii  Engineer's  Pocket  BooR.'* 


CIRCLES. 

TABLE  1  OF  CIRCLES. 
Diameters  in  units  and  eighths,  &c. 

Circumferences  or  areas  intermediate  of  those  in  this  table,  may  be  fonnd  by  sim- 
ple arithmetical  proportion.  No  errors. 


Diam    Circumf.      Area. 

j 

Diam. 

Circumf.    Area. 

Diam. 

Circumf.    Area. 

' 

Diam. 

Circumf. 

Area 

1-64 

.049087     .00019 

3.     H 

10.9956         9.621 

10*  i  31.8086  i   80.516 

19^4 

60.4757 

291.04 

1-3-2 

.098175     .00077 

9-16 

11.1919        9.9678 

X 

32.2013 

82.516 

% 

60.8684 

294.83 

3-64 

.147262     .00173 

K 

11.3883        10.321 

K 

32.5940 

84.541 

M 

61.2611 

298.65 

1-16 

.196350     .00.507 

11-16 

11.5846  j     10.680 

M 

32.9867 

86.590 

N 

61.6538 

302.49 

3-32 

.294524:    .00690 

h 

11.7810      11.045 

33.3794 

88.664 

% 

62.0465 

306.35 

M 

.3926991    .01227 

13-16 

11.9773       11.410 

H 

33.7721 

90.763 

% 

62.4392 

310.24 

5-32 

.490874     .01917 

X 

12.1737       11.793 

% 

34.1648 

92.886 

20. 

62.8319 

314.16 

3-16 

589049     .0:1761 

15-16 

12.3700      12.177 

11. 

34.5575 

95.033 

H 

63.2246 

318.10 

7-32 

.687223      .0.-J75S 

4.            12.56:;  I       12.  JIM! 

X 

34.9502 

97.205 

VA. 

63.6173 

322.06 

M 

.785398     .04  »0) 

MS     12.7o27       12.90.' 

/4 

35.3429 

99.402 

% 

64.0100 

326.05 

9-32 

.885573     .0.-5213 

%      1295JI  i    r:.3<>4 

H 

35.7356 

101.62 

3 

64.4026 

330.06 

5-16 

.98(748     .071)70 

3-lii      1.5.1554       13.772 

H 

30.1283 

103.87 

*A 

64.7953 

334.10 

11-32 

1.07992       j):i2^i 

14     13.3518      14.186 

% 

36.5210 

106.14 

% 

65.1880 

338.16 

M 

1.17810       .11015 

5-16     13.5481      14.607 

H 

36.9137 

10*.  43 

y» 

65.5807 

342.25 

13-32 

1.27627       .12:*!-' 

:i8      1.5.711.")       15.0  5.J. 

y» 

37.3064 

110.75 

21. 

65.9734 

346.36 

7-16 

1.37445       .150:5! 

7-ltJ      1394H      15.46(5 

12. 

37.69'Jl 

113.10 

M 

66.3661 

350.50 

15-32 

1.47262       .17257 

?4.    14.1.572       15.904 

H 

38.0918 

115.47 

J4 

66.7588 

354.66 

M 

1.57080       .19835 

9-16,    14.3.555      16.:H9 

YA. 

38.4*45     117.86 

M 

67.1515 

358.84 

17-32 

1.66897       .2216. 

%•    14.52  )J      16.800 

% 

3S.S772     120.28 

% 

67.5442 

363.05 

9-  IB     1.76715       .2U-y) 

11-16     14.7282      17  257 

% 

:;:»  2!)!!1)     122.72 

% 

67.9369 

367.28 

19-32     1.S6532       .27')^ 

%      14.92215      17.721 

% 

39.15626    125.19 

% 

68.3296 

371.54 

%     1.9S35U       .303-0 

13-  1.  i     15.1  IS.) 

18.190 

?i 

40.0553    127.68 

% 

68.7223 

375.83 

21-32     2.06167       .3!^2t 

yB     15.  51  5-  J 

18.665 

% 

40.4480     130.19 

22.          69.1150 

380.13 

11-16 

2.15984       .37122 

15-16     15.5116 

19.H7 

13. 

40.8407    132.73 

%    \  69.5077 

884.46 

23-32 

2.25802       .4U574 

5.           15.703J 

19.635 

M 

41.2334     135.30 

V\ 

69.9004 

388.82 

K 

2.35619       .4U7:> 

1-16     15.M45 

20.12J 

W 

41.6261 

137.89 

% 

70.2931 

393.20 

25-32     2.45437       .479.57 

X     16.101)7 

20.629 

% 

42.0188 

140.50 

H 

70.6858 

397.61 

13-16     2.55254       .51  8  W 

3-16     16.2970 

21.135 

H 

42.4115 

143.14 

% 

71.0785 

402.04 

27-32     2.65072       .55911 

Yi      16.49,54  :    21.648 

K 

42.8042 

145.80 

% 

71.4712 

406.49 

J*     2.74889 

.60132 

5-16     16.fi897 

22.166 

% 

43.1969 

148.49 

H 

71.8639 

410.97 

29-32     2.84707 

.64504 

K      16.8861 

22.691 

% 

43.5896 

151.20 

23 

72.2566 

415.48 

15-16 

2.94524 

.6902:) 

7-16     17.0324 

23.221 

14 

43.9823 

153.94 

M 

72.6493 

420.00 

31-32 

3.04342 

.73708 

%\    17.2788 

28.758 

X 

44.3750 

156.70 

73.0420 

424.56 

1. 

3.14159 

.78540 

9-16      17.4751 

24.301 

y± 

44.7677 

159.48 

H 

73.4347 

429.13 

1-16 

3.33794 

.88664 

%     17.6715 

24.850 

% 

45.1604 

162.30 

^ 

73.8274 

433.74 

H     3.53429 

.99402 

11-16     17.8678 

25.406 

¥ 

45.5531 

165.13 

% 

74.2201 

438.36 

3-16     3.73064 

1.1075 

%     18.0642 

25.967 

45.9458 

167.99 

H 

74.6128 

443.01 

Y±<  3.92699 

1.2272 

13-16     18.2605 

26.535 

3^ 

46.3385 

170.87 

y» 

75.0055 

447.69 

5-16     4.12334 

1.3530 

%     18.4569 

27.109 

H 

46.7312 

173.78 

75.3982 

452.39 

%     431969 

1.4849 

15-16     18.6532 

27.688 

15. 

47.1239 

176.71 

H 

75.7909 

457.11 

7-16    4.51604 

1.6230 

6. 

18.8496      28.274 

M 

47.5166 

179.67 

y\ 

76.1836 

461.86 

^     4.71239 

1.7671 

X     19.2423  1   29.465 

47.9093 

182.65 

H 

76  5763 

466.64 

9-16     4.90874 

1.9175 

J4  j    19.6350  ;   30.680 

% 

48.3020 

185.66 

y* 

76.9690 

471.44 

K     5.10509 

2.0739 

%!    20.0277 

31.919 

% 

48.6947 

188.69 

% 

77.3617 

476.26 

11-16    5.30144 

2.2365 

K      20.4204 

33.183 

% 

49.0874 

191.75 

H 

77.7544 

481.11 

%     5.49779 

2.4053 

H 

20.8131 

34.472 

% 

49.4801 

194.83 

X 

78.1471 

485.98 

13-16    5.69414 

2.5S02 

% 

21.2058 

35.785 

X 

49.8728 

197.93 

25 

78.5398 

490.87 

Jg     5.89049 

2.7612 

K 

21.5984 

37.122 

16. 

50.2655 

201.06 

M 

78.9325 

495.79 

15-16    6.08684 

2.9483 

7. 

21.9911 

38.485 

H 

50.6582 

204.22 

y\ 

79.3252 

500.74 

2.           6  28319 

3.1416 

H 

22.3838 

39.871 

H 

51.0509 

207.39 

% 

79.7179 

505.71 

1-16    6.47953 

3.3410 

H     22.7765 

41.282 

% 

51.4436 

210.60 

y* 

80.1106 

510.71 

K     6.67588 

3.5466 

*     23.1692 

42.718 

K 

51.8363 

213.52 

% 

80.5033 

515.72 

3-16    687223 

3.75S3 

K     23.5619 

44.179 

% 

52.2290 

217  08 

% 

80.8960 

520.77 

H     7.06858 

3.9761 

%  !    23.9546 

45664 

H 

52.6217 

220.35 

% 

81.2887 

525.84 

516     7.26493 

4.2000 

%i    24.3473 

47.173 

% 

53.0144 

223.65 

26 

81.6814 

530.93 

%     7.46128 

4.4301 

X 

24.7400 

48.707 

17. 

53.4071 

226.98 

H 

82.0741 

536.05 

7-16     7.65763     4.6664 

8. 

25.1327 

50.265 

M 

53.7998 

230.33 

y*. 

82.4668 

541.19 

K     7.85398     4.9087 

X 

25.5254 

51.849 

y± 

54.1925 

233.71 

X 

82.8595 

546.35 

9-16    8.05033    [5.1572 

y* 

25  9181 

53.456 

% 

54.5852 

237.10 

% 

83.2522 

551.55 

^     8.24668    i  5.4119 

H 

26.3108 

55.088 

H 

54.9779 

240.53 

K 

83.6449 

556.76 

11-16    8.44303 

5.6727 

X 

26.7035 

56.745 

% 

55.3706 

243.98 

X 

84.0376 

562.00 

V\  8.63938 

5.9396 

% 

27.0962 

58.426 

X 

55.7633 

247.45 

% 

84.4303 

567.27 

13-16    8.83573 

6.2126 

% 

27.4889 

60.132 

% 

56.1560 

250.95 

27 

84.8230 

572.56 

X    9.03208 

6.4918 

% 

27.8816 

61.862 

18. 

56.5487 

254.47 

U 

85.2157 

577.87 

15-16    9.22843 

6.7771 

9. 

28.2743 

63.617 

Ml 

56.9414 

258.02 

3 

85.6084 

583.21 

«.           9.42478 

7.0686 

M 

28.6670 

65.397 

^ 

57.3341 

261.59 

% 

86.0011 

588.57 

1-16     9.62113 

7.3662 

M 

29.0597 

67.201 

N 

57.7268 

265.18 

% 

86.3938 

593.96 

J^     9.81748 

7.6699 

% 

29.4524 

69.029 

H 

58.1195 

268.80 

N 

86.7865 

599.37 

3-16  10.0138 

7.9798 

M 

29.8451 

70.882 

N 

58.5122 

272.45 

K 

87.1792 

604.81 

%  10.2102 

8.2958 

N 

30.2378 

72.760 

% 

58.9049 

276.12 

% 

87.5719 

610.27 

5-16  10.4065 

8.6179 

K 

30.6305 

74662 

% 

59.2976 

279.81 

28 

87.9646 

615.75 

%   10.6029 

8.9462 

X 

31.0232 

76.589 

19. 

59.6903 

283.53 

H 

88.3573 

621.2S 

T-  16  10.7992 

9.2806 

10. 

31.4159 

78.540 

» 

60.0830 

287.27 

y* 

88.7500 

636.84 

170  TABLE  NO.  71— COST. 

From  Trautwine's  "Civil  Engineer's  Pocket  Book." 


CIRCLES. 

TABLE  1  OF  CIRCXES— (Continued). 
Diameters  in  units  anil  eighths,  Ac. 


. 

Area. 

Diam. 

Uiroami.     Area. 

M& 

89.1427  j    632.36 

38. 

119.381    :      134.1 

47%    !    149.618 

1781.4 

O'xi 

179.856  !    2574.2 

| 

89.5354 

637.94 

X 

119.773 

141.6 

150.011 

1790.8 

xi 

180.249 

2585-4 

89.9281 

643.55 

120.166 

149.1 

y 

150.404 

1800.1 

xi 

180.642 

2596.7 

% 

90.3208 

649.18 

% 

120.559 

156.6 

48 

150.796 

1809.6 

xi 

181.034 

2608.0 

% 

90.7135 

654.84 

120.951 

164.2 

xi 

151.189 

1819.0 

34 

181.427 

2619.4 

S9. 

91.1062 

660.52 

% 

21.344         171.7 

i 

1.51.582 

1828.5 

y8        181.820 

2630.7 

H 

91.4989 

666.23 

% 

21.737 

179.3 

iL 

151.975       1837.9 

5S.          182.212 

2642.1 

91.8916 

671.96 

% 

22.129 

186.9 

\o 

152.367 

1847.5 

X       182.605 

2653.5 

H 

92.2843 

677.71 

39. 

22.522 

194.6 

% 

152.760 

1857.0 

182.998 

2664.9 

i^ 

92.6770 

683.49 

x« 

22.915 

202.3 

153.153 

1866.5 

% 

183.390 

2676.4 

xii 

93.0697 

689.30 

xi 

23.308         210.0 

y 

153.545 

1876.1 

i^ 

183.783 

2687.8 

x4 

93.4624 

695.13 

% 

23.700         217.7 

49. 

153.938 

1885.7 

RX 

184.176 

2699.3 

% 

93.8551 

700.98 

y* 

24.093  '      225.4 

l/i 

154.331 

1895.4 

84 

184.569 

2710.9 

30. 

94.2478 

706.86 

% 

24.486         233.2 

i^ 

154.723 

1W)5'.0 

TX 

184.961 

2722.4 

H 

94.6405 

712.76 

% 

24.878         241.0 

N 

155.116 

1914.7 

59.          185.354 

2734.0 

95.0332 

718.69 

% 

25.271         248.8 

x^ 

155.509 

1924.4 

rx 

185.747 

2745.6 

x'S 

95.4259 

724.64 

40. 

23.664         256.6 

% 

155.902 

1934.2 

Ji 

186.139 

2757.2 

% 

95.8186 

730.62 

y*, 

•_r,.n5»i         264.5 

?4 

156.294 

1943.9 

N 

1*6.532 

2768.8 

8* 

96.2113 

736.62 

'4          26.449 

272.4 

% 

156.687 

1953.7 

y* 

186.925 

2780.5 

96.6040 

742.64 

3/8          26.842 

280.3 

50. 

157.080 

1963.5 

187.317 

2792.2 

yt 

96.9967 

748.69 

hi          27.235 

288.2 

i^j 

157.472 

1973.3 

% 

187.710 

2803.9 

81. 

97.3894 

754.77 

%         27.627 

296.2 

i  ' 

157.865 

1983.2 

y 

188.103 

2815.7 

i* 

97.7821 

760.87 

?i         28.020 

304.2 

^8 

158.258 

1993.1 

60. 

188.496 

2827.4 

98.1748 

766.99 

%        128.413 

312.2 

LJ 

158.650 

2003-0 

iz 

188.888 

2839.2 

% 

98.5675 

773.14 

41.          128.805 

320.3 

% 

159.043 

2012.9 

y 

189.281 

2851.0 

j^ 

98.9602 

779.31 

129  198 

328.3 

H 

159.436 

2022.8 

% 

189.674 

2862.9 

% 

99.3529 

785.51 

2 

129.591 

336.4 

% 

159.829 

2032.8 

/£ 

190.066 

2874.8 

^i 

99.7456 

791.73 

% 

129.983 

344.5 

51. 

160.221 

2042.8 

BX 

190.459 

2886.6 

W 

100.138 

797.98 

% 

130.376 

352.7 

\z 

160.614 

2052.8 

% 

190.852 

2898.6 

82. 

100.531 

804.25 

%       130.769 

1360.8 

IX 

161.007 

2062.9 

191.244 

2910.5 

/^ 

100.924 

810.54 

H    \    131.161 

369.0 

x8 

161.399 

2073.0 

61. 

191.637 

2922.5 

i,' 

101.316 

816.86 

K        131.554 

377.2 

161.792 

2083.1 

192.030 

2934.5 

y 

101.709 

823.21 

42.          131.947 

385.4 

M 

162.185 

2093.2 

M 

192.423 

2946.5 

¥1 

102.102 

829.58 

X      I32.:uo 

393.7 

162.577 

2103.3 

H 

192.815 

2958.5 

RZ 

102.494 

835.97 

>4    \    132.732 

402.0 

rx 

162.970 

2113.5 

193.208 

2970.6 

$£ 

102.887 

842.39 

*g        133.125 

410.3 

52. 

163.363 

2123.7 

RX 

193.601 

2982.7 

rx 

103.280 

848.83 

14       133.518 

418.6 

H 

163.756 

2133.9 

xi 

193.993 

2994.8 

33. 

103.673 

855.30 

xg        133.910 

427.0 

164.148 

2144.2 

% 

194.386 

3006.9 

H 

104.065 

861.79 

34    |    134.303 

435.4 

% 

164.541 

2154.5 

62. 

194.779 

3019.1 

i^ 

104.458 

868.31 

%    !    134.696 

443.8 

yd 

164.934 

2164.8 

H 

195.171 

3031.3 

% 

104.851 

874.85 

43.      !    135.088        452.2 

% 

165.326 

2175.1 

y\ 

195.564 

3043.5 

N 

105.243 

881.41 

xi       135.481         460.7 

% 

165.719 

2185.4 

% 

195.957 

3055.7 

105.636 

888.00 

M       135.874 

469.1 

% 

166.112 

2195.8 

% 

196.350 

3068.0 

9i 

106.029 

894.62 

28        136.267 

477.6 

53. 

166.504 

2206.2 

% 

196.742 

3080.3 

V 

106.421 

901.26 

%        136.659 

1486.2 

166.897   i   2216.6 

% 

197.135 

3092.6 

34. 

106.814    |    907.92 

K       137.052 

1494.7 

^ 

167.290       2227.0 

% 

197.528 

3104.9 

Ji 

107.207 

914.61 

137.445 

1503.3 

167.683   i    2237.5 

63. 

197.920 

3117.2 

.  i/ 

107.600 

921.32 

xfc 

137.837 

1511.9 

X 

168.075  !    2248.0 

xfi 

198.313 

3129.6 

% 

107.992        928.06 

44. 

138.230 

1520.5 

% 

168.468       2258.5 

IX 

198.706 

3142.0 

^ 

108.385        934.82 

\z 

138.623 

1529.2 

% 

168.861       2269.1 

x"8 

199.098 

3154.5 

N 

108.778 

941.61 

Y 

139.015 

1537.9 

% 

169.253   i    2279.6 

V4 

199.491 

3166.9 

109.170        948.42 

% 

139.408 

1546.6 

54. 

169.646       2290.2 

xi 

199.884 

3179.4 

*x 

109.563        955.25 

ix  • 

139.801 

1555.3 

% 

170.039      2300.8 

xi 

200.277 

3191.9 

85. 

109.956        9(52.11 

xi 

140.194 

1564.0 

IX 

170.431   i    2311.5 

% 

200.669 

3204.4 

110.348         969.00 

9i 

140  586 

1572.8 

% 

170.824       2322.1 

64. 

201.062 

3217.0 

34 

110.741    I    975.91 

TX 

140.979  !    1581.6 

1^ 

171.217       2332.8 

xi 

201.455 

3229.6 

^/ 

111.134 

982.84 

45. 

141.372       1590.4 

Y 

171.609       2343.5 

y\ 

201.847 

3242.2 

s 

111.527 

989.80 

N 

141.764       1599.3 

% 

172.002       2354.3 

% 

202.240 

3254.8 

tx 

111.919 

996.78 

42.157       1608.2 

y 

172.395 

2365.0 

x*> 

202.633 

3267.5 

% 

112.312 

1003.8 

az 

42.550 

1617.0 

55. 

172.788 

2375.8 

% 

203.025 

3280.1 

TX 

112.705 

1010.x 

IX 

42.942 

1626.0 

173.180 

2386.6 

H 

203.418 

3292.8 

M. 

113.097 

1017.9 

H 

43.335 

1634. 

xi 

173.573 

2397.5 

203.811 

3305.6 

113.490 

1025-0 

43.728 

1643. 

173.966 

2408.3 

65. 

204.204 

3318.3 

M 

113.883 

10321 

K 

44.121 

1652. 

X 

174.358 

2419.2 

% 

204.596 

3331.1 

«/ 

114.275 

1039.2 

46 

44.513 

1661. 

174.751       2430.1 

y\ 

204.989 

3343.9 

i^ 

114.668 

1046.3 

M 

44.906 

1670. 

H 

175.144       2441.1 

N 

205.382 

3356.7 

RX 

115.061 

1053.5 

45.299 

1680. 

TX 

175.536      2452.0 

x^ 

205.774 

3369.6 

5i 

115.454 

1060.7 

% 

45.691 

1689. 

Mk 

175.929      2463.0 

N 

206.167 

3382.4 

7X 

115.846 

1068.0 

ix 

46.084 

1698. 

xf) 

176.322       2474.0 

206.560 

3395.3 

87. 

116.239 

1075.2 

fcX 

46.477          707. 

1^ 

176.715       2485.0 

K 

206.952 

3408.2 

116.632 

1082.5 

% 

46.869         716. 

^8 

177.107       2496.1 

66. 

207.345 

3421.2 

M 

117.024 

1089.8 

TX 

47.2H2         725. 

^ 

177.500       2507.2 

% 

207.738 

3434.2 

N 

117.417 

1097.1 

47. 

47.655         734. 

N 

177.893       2518.3 

% 

208.131 

3447.2 

117.810 

1104.5 

4,SO;»>         744. 

* 

178.285       2529.4 

% 

208.523 

3460.2 

118.202    ;  1111.* 

48.440         753. 

178.678       2540.6 

y* 

208.916 

3473.2 

•/ 

118.596       1119.2 

% 

48.833         762. 

57.  * 

179.071       2551.8 

N 

209.309 

3486.3 

K 

J.  18.988    i  1126.7 

H 

149.226         772. 

179.463       2563.0 

N 

209.701 

3499.4 

TABLE  NO.  71— CON. 


171 


From  Trautwiue**  -4Jivii  Engineer'*  iPoeket  Book." 

CIBCLES. 

TABLE  1  OF  CIRCI.ES-(Continued). 
Diameter**  in  units  and  eighths,  Ac. 


Diam. 

Circumf. 

Area. 

Diam. 

Circumf.     Area. 

Diam. 

Circumf. 

Area. 

Diam. 

Circumf. 

Area. 

~% 

210.094  i    3512.5 
210.487       3525.7 

75^; 

236.405       4447.4 
236.798   !    4462.2 

^8jg! 

262.716 
263.108 

5492.4 
5508.8 

92. 

289.027       6647.6 
289.419      6665.7 

IX 

210.879      3538.8 

1^; 

237.190       4477.0 

•v 

263.501 

5525.3 

IX 

289.812 

6683.8 

^ 

211.272 

3552.0 

xi 

237.583       4491.8 

84. 

263.894 

5541.8 

xi 

290.205 

6701.9 

xi 

211.665 

3565.2 

H 

237.976       4506.7 

xi 

264.286 

5558.3 

xi 

290.597       6720.1 

xi 

212.058 

3578.5 

rx 

838.368 

4521.5 

264.679 

5574.8 

xi 

290.990      6738.2 

xi 

212.450 

3591.7 

76. 

•238.761 

4536.5 

xi 

265.072 

5591.4 

H 

291.383 

6756.4 

Ji 

212.843 

3605.0 

239.154 

4551.4 

265.465 

5607.9 

291.775 

6774.7 

JX 

213.236 

3618.3 

H 

239.546 

4566.4 

xi 

265.857 

5624.5 

93.    ' 

292.168 

6792.9 

68. 

213.628 

3631.7 

% 

239.939 

4581.3 

xi 

266.250 

5641.2 

xi 

292.561       6811.2 

xi 

214.021 

3645.0 

240.332 

45%.  3 

xi 

266.643 

5657.8 

292.954       682V.5 

214.414 

3658.4 

xi 

240.725 

4611.4 

85. 

267.035 

5674.5 

xi 

293.346      6847.8 

xi 

214.806 

3671.8 

xi 

241.117 

4626.4 

xi 

267.428 

5691.2 

xi 

293.739  j   6866.1 

xi 

215.199 

3685.3 

•u 

241.510 

4641.5 

k 

267.821 

5707.9 

xi 

294.132      6884.5 

215.592 

3698.7 

77. 

241.903 

4656.6 

xi 

268.213 

5724.7 

H 

294.524       6902.9 

a// 

215.984 

3712.2 

242.295 

4671.8 

xi 

268.606 

5741.5 

294.917 

6921.3 

>i 

216.377 

3725.7 

IX 

242.688 

4686.9 

268.999 

5758.3 

94. 

295.310 

6939.8 

69. 

216.770 

3739.3 

xi 

243.081 

4702.1 

x^ 

269.392 

5775.1 

xi 

295.702  !    6958.2 

xi 

217.163 

3752.8 

}*> 

243.473 

4717.3 

xi 

269.784 

5791.9 

IX 

296.095 

6976.7 

217.555 

3766.4 

xi 

243.866 

4732.5 

86. 

270.177 

5808.8 

xi 

296.488 

6995.3 

9i 

217.948 

3780.0 

H 

244.259 

4747.8 

xi 

270.570 

5825.7 

xi 

2%.881 

7013.8 

218.341 

3793.7 

244.652 

4763.1 

x4 

270.962 

5842.6 

% 

297.273 

7032.4 

2i 

218.733 

3807.3 

78. 

245.044 

4778.4 

N 

271.355    5859.6 

* 

297.666 

7051.0 

3i 

219.126 

3821.0 

^ 

•245.437        4793.7 

271.748    5876.5 

298.059 

7069.6 

JX 

219.519 

3834.7 

xi 

•245.830       4809.0 

xi 

272.140     5893.5 

95. 

298.451 

7088.2 

70. 

219.911 

3848.5 

246.222       48'24.4 

h 

272.533 

5910.6 

xi 

298.844 

7106.9 

220.304 

3862.2 

xi 

246.615       4839.8 

272.926 

5927.6 

x4 

299.237 

7125.6 

IX 

220.697 

3876.0 

xi 

247.008       4855.2 

87. 

273.319    5944.7 

N 

299.629 

7144.3 

xi 

221.090 

3889.8 

% 

247.400       4870.7 

273.711 

5961.8 

N 

300.022 

7163.0 

xi 

221.482 

3903.6 

247.793       4886.2 

H 

1274.104     5978.9 

xi 

300.415 

7181.8 

xi 

221.875 

3917.5 

79. 

248.186       4901.7 

% 

274.497     5996.0 

8 

300.807 

7200.6 

5 

222.268 

3931.4 

% 

248.579       4917.2 

274.889   !  6013.2 

V     301.200 

7219.4 

H 

222.660 

3945.3 

y* 

248.971       4932.7 

xi 

275.282 

6030.4 

96.          301.593 

1238.2 

71. 

223.053 

3959.2 

% 

249.364       4948.3 

9i 

275.675 

6047.6 

IX 

301.986 

7257.1 

xi 

2-23.446 

3973.1 

249.757       4963.9 

Ji 

276.067 

6064.9 

H 

302.378 

72760 

223.838 

3987.1 

Y 

250.149       4979.5 

88. 

276.460 

6082.1 

% 

302.771 

7294.9 

xi 

224.231 

4001.1 

H 

250.542       4995.2 

276.853 

6099.4 

303.164 

7313.8 

3^ 

224.624 

4015.2 

xi 

250.935       5010.9 

xi 

!    277.246 

6116.7 

xi 

303.556 

7332.8 

xi 

225.017 

4029.2 

80. 

251.327       5026.5 

277.638 

6134.1 

H 

303.949 

7351.8 

a^ 

225.409 

4043.3 

xi 

251.720  !    5042.3 

y 

278.031 

6151.4 

304.342 

7370.8 

x 

225.802 

4057.4 

252.113  !    5058.0 

xi 

278.424    6168.8 

97.    * 

304.734 

7389.8 

72. 

226.195 

4071.5 

xi 

252.506 

5073.8 

a/ 

278.816    6186.2 

xi 

305.127 

7408.9 

226.587 

4085.7 

252.898 

5089.6 

xi 

i    279.209  |  6203.7 

305.520 

7428.0 

M 

226.980 

4099.8 

xi 

253.291 

5105.4 

89. 

279.602    6221.1 

xi 

305.913 

7447.1 

xi 

227.373 

4114.0 

253.684 

5121.2 

,    279.994    6238.6 

xi 

306.305 

7466.2 

xi 

227.765 

4128.2 

•u 

254.076 

5137.1 

y* 

280.387    6256.1 

xi 

306.698 

7485.3 

N 

228.158 

4142.5 

81. 

254.469 

5153.0 

% 

280.780    6273.7 

307.091 

7504.5 

»xj 

228.551 

4156.8 

254.862 

5168.9 

xi 

!    281.173    6291.2 

V 

307.483 

7523.7 

H 

228.944 

4171.1 

M 

255.254 

5184.9 

281.565    6308.8 

98.    8 

307.876 

7543.0 

73. 

229.336 

4185.4 

255.647 

5200.8 

N 

281.958     6326.4 

xi 

308.269 

7562.  J 

229.729 

4199.7 

xi 

256.040 

5216.8 

?i 

282.351     6344.1 

N 

308.661 

7581.5 

y* 

230.122 

4214.1 

N 

256.433 

5232.8 

90. 

282.743     6361.7 

s 

309.054 

7600.8 

xi 

230.514 

4228.5 

ji 

256.825 

5248.9 

xi 

283.136    6379.4 

N 

309.447   \    7620.1 

230.907 

4242.9 

Ji 

257.218 

5264.9 

|    283.529    6397.1 

%     309.840       7639.5 

xi 

231.300 

4257.4 

82. 

257.611       5281.0 

xi 

283.921     6414.9 

&i    310.232  i    7658.9 

J^ 

231.692 

4271.8 

xi 

258.003       5297.1 

X* 

284.314     6432.6 

xi 

310.625       7678.3 

xi 

232.085 

4286.3 

>i 

258.3%       5313.3 

xi 

284.707     6450.4 

99.    " 

311.018      7697.7 

74. 

232.478 

4300.8 

xi 

258.789  >    5329.4 

x4 

285.100  .6468.2 

xi 

311.410      7717.1 

232.871 

4315.4 

259.181       5345.6 

xi 

285.492     6486.0 

311.803       7736.6 

14 

233.263 

4329.9 

xi 

259.574       5361.8 

91. 

285.885     6503.9 

xi 

312.1%      7756.1 

ft 

233.656 

4344.5 

xi 

259.%7       5378.1 

286.278     6521.8 

IX 

312.588      7775.6 

% 

234.049 

4359.2 

Ji 

260.359  1    5394.3 

j/ 

286.670     6539.7 

xi 

312.981       7795.2 

N 

234.441 

4373.8 

83. 

260.752       5410.6 

xi 

287.063     6557.6 

II 

313.374      7814.8 

« 

234.834 

4388.5 

^i 

261.145       5426.9 

Ix. 

287.456    6575.5 

?i 

313.767      7834.4 

235.227 

4403.1 

y* 

261.538       5443.3 

R/ 

!    287.848     6593.5 

100. 

314.159 

7854.0 

75. 

235.619 

4417.9 

xi 

261.930 

5459.6 

a/ 

288.241     6611.5 

ft 

236.012 

4432.6 

X 

262.323 

5476.0 

* 

288.634    6629.6 

172  TABLE  NO.  72. 

From  Trantwine's  "Civil  Engineer's  Pocket  Book." 

CIRCLES. 

TABLE  2   OF  CIRCLES. 
Diameters  in  units  and  tenths. 


Dia. 

Circumf. 

Area. 

Dia. 

Circumf. 

Area. 

Dia. 

Circumf. 

Area. 

0.1 

.314159 

.007854 

6.3 

19.79203 

31.17245 

12.5 

39.26991 

122.7185 

.2 

.628319 

.031416 

.4 

20.10619 

32.16991 

.6 

39.58407 

124.6898 

.3 

.942478 

.070686 

.5 

20.42035 

33.18307 

.7 

39.89823 

126.6769 

.4 

1.256637 

.125664 

.6 

20.73451 

34.21194 

.8 

40.21239 

128.6796 

.5 

1.570796 

.196350 

.7 

21.04867 

35.25652 

.9 

40.52655 

130.6981 

.6 

1.884956 

.282743 

.8 

21.36283 

36.31681 

13.0 

40.84070 

132.7323 

.7 

2.199115 

.384845 

.9 

21.67699 

37.39281 

.1 

41.15486 

134.7822 

.8 

2.513274 

.502655 

7.0 

21.99115 

38.48451 

.2 

41.46902 

136.8478 

.9 

2.827433 

.636173 

.1 

22.30531 

39.59192 

;3 

41.78318 

138.9291 

1.0 

3.141593 

.785398 

.2 

22.61947 

40.71504 

.4 

42.09734 

141.0261 

.1 

3.455752 

.950332 

.3 

22.93363 

41.85387 

.5 

42.41150 

143.1388 

.2 

3.769911 

1.13097 

.4 

23.24779 

43.00840 

.6 

42.72566 

145.2672 

.3 

4.084070 

1.32732 

.5 

23.56194 

44.17865 

.7 

43.03982 

147.4114 

.4 

4.398230   1.53938 

.6 

23.87610 

45.36460 

.8 

43.35398 

149.5712 

.5 

4.712389  !  1.76715 

.7 

24.19026 

46.56626 

.9 

43.66814 

151.7468 

.6 

5.026548  i  2.01062 

.8 

24.50442 

47.78362 

14.0 

43.98230 

153.9380 

.7 

5.340708  :  2.26980 

.9 

24.81858 

49.01670 

.1 

44.29646 

156.1450 

.8 

5.654867   2.54469 

8.0 

25.13274 

50.26548 

.2 

44.61062 

158.3677 

.9 

5.969026   2.83529 

.1 

25.44690 

51.52997 

.3 

44.92477 

160.6061 

2.0 

6.283185   3.14159 

.2 

25.76106 

52.81017 

.4 

45.23893 

162.8602 

.1 

6.597345   3.46361 

.3 

26.07522 

54.10608 

.5 

45.55309 

165.1300 

.2 

6.911504  !  3.80133 

.4 

26.38938 

55.41769 

.6 

45.86725 

167.4155 

.3 

7.225663   4.15476 

.5 

26.70354 

56.74502 

.7 

46.18141 

169.7167 

.4 

7.539822 

4.52389 

.6 

27.01770 

58.08805 

.8 

46.49557 

172.0336 

.5 

7.853982 

4.90874 

.7 

27.33186 

59.44679 

.9 

46.80973 

174.3662 

.6 

8.168141   5.30929 

.8 

27.64602 

60.82123 

15.0 

47.12389 

176.7146 

.7 

8.482300   5.72555 

.9 

27.96017 

62.21139 

.1 

47.43805 

179.0786 

.8 

8.796459  j  6.15752 

9.0 

28.27433 

63.61725 

.2 

47.75221 

181.4584 

.9 

9.110619  ,  6.60520 

.1 

28.58849 

65.03882 

.3 

48.06637 

183.8539 

8.0 

9.424778   7.06858 

.2 

28.90265 

66.47610 

.4 

48.38053 

186.2650 

.1 

9.738937  !  7.54768 

.3 

29.21681 

67.92909 

.5 

48.69469 

188.6919 

.2 

10.05310  !  8.04248 

.4 

29.53097 

69.39778 

.6 

49.00885 

191.1345 

.3 

10.36726  ;  8.55299 

.5 

29.84513 

70.88218 

.7 

49.32300 

193.5928 

.4 

10.68142  i  9.07920 

.6 

30.15929 

72.38229 

.8 

49.63716 

196.0668 

.5 

10.99557   9.62113 

.7 

30.47345 

73.89811 

.9 

49.95132 

198.5565 

.6 

11.3097^ 

10.17876 

.8 

30.78761 

75.42964 

16.0 

50.26548 

201.0619 

.7 

11.62389 

10.75210 

.9 

31.10177 

76.97687 

.1 

50.57964 

203.5831 

.8 

11.93805 

11.34115 

10.0 

31.41593 

78.53982 

.2 

50.89380 

206.1199 

.9 

12.25221 

11.94591 

.1 

31.73009 

80.11847 

.3 

51.20796 

208.6724 

4.0 

12.56637 

12.56637 

.2 

32.04425 

81.71282 

.4 

51.52212 

211.2407 

^ 

12.88053 

13.20254 

.3 

32.35840 

83.32289 

.5 

51.83628 

213.8246 

'.2 

13.19469 

13.85442 

.4 

32.67256 

84.94867 

.6 

52.15044 

216.4243 

.3  1  13.50885 

14.52201 

.5 

32.98672 

86.59015 

.7 

52.46460 

219.0397 

.4  13.82301 

15.20531 

.6 

33.30088 

88.24734 

.8 

52.77876 

221.6708 

.5  14.13717 

15.90431 

.7 

33.61504 

89.92024 

.9 

53.09292 

224.3176 

.6  |  14.45133 

16.61903 

.8 

33.92920 

91.60884 

17.0 

53.40708 

226.9801 

.7 

14.76549 

17.34945 

.9 

34.24336 

93.31316 

.1 

53.72123 

229.6583 

.8 

15.07964 

18.09557 

11.0 

34.55752 

-  95.03318 

.2 

54.03539 

232.3522 

.9 

15.39380 

18.85741 

.1  34.87168 

96.76891 

.3 

54.34955 

235.0618 

5.0 

15.70796 

19.63495 

.2 

35.18584 

98.52035 

.4 

54.66371 

237.7871 

.1 

16.02212 

20.42821 

.3 

35.50000 

100.2875 

.5 

54.97787 

240.5282 

.2 

16.33628 

21.23717 

.4 

35.81416 

102.0703 

.6 

55.29203  i  243.2849 

.3 

16.65044 

22.06183 

.5 

36.12832 

103.8689 

.7 

55.60619  !  246.0574 

.4 

16.96460 

22.90221 

.6 

36.44247 

105.6832 

.8 

55.92035 

248.8456 

.5 

17.27876. 

23.75829 

.7 

36.75663 

107.5132 

.9 

56.23451 

251.6494 

.6 

17.59292 

24.63009 

.8 

37.07079 

109.3588 

18.0 

56.54867 

254.4690 

.7 

17.90708 

25.51759 

.9 

37.38495 

111.2202 

.1 

56.86283 

257.3043 

.8 

18.22124 

26.42079 

12.0 

37.69911 

113.0973 

.2 

57.17699 

260.1553 

.9 

18.53540 

27.33971 

.1 

38.01327 

114.9901 

.3 

57.49115 

263.0220 

&o 

18.84956 

28.27433 

.2 

38.32743 

116.8987 

.4 

57.80530 

265.9044 

.1 

19.16372 

29.22467 

.3 

38.64159 

118.8229 

.5 

58.11946 

268.8025 

.2 

19.47787 

30.19071 

.4 

38.95575 

120.7628 

.6 

58.43362 

271.7163 

TABLE  NO.  72— CON.  173 

From    I  i  .mi  \\  in<   s  ••<  ivil  Engineer's  Pocket  Book." 

CIRCLES. 

TABLE  2  OF   CIRCLES— (Continued). 
in  uiiifs  and  tenths. 


Dia. 

Cireumf. 

Area. 

Dia. 

Circumf. 

Area. 

Dia. 

Circumf. 

Area. 

18.7 

58.74778 

274.6459 

•24.9 

78.22566 

486.9547 

31.1 

97.70353 

759.6450 

.8 

59.ur>liq 

277.5911 

25.0  78.53982 

490.8739 

.2 

98.01769 

764.5380 

.9 

59.37610 

280.5521 

.1  1  78.85398 

494.8087 

.3 

98.331  85 

769.4467 

19.0 

59.69026   283.5287 

.2  79.16813 

498.7592 

.4 

98.64601 

774.3712 

.1 

r,<Mn,442   286.5211 

.3  79.18229 

502.7255 

.5 

98.96017 

779.3113 

.2 

60.31858   289.5292 

.4   79.79645 

506.7075 

.6 

99.27433 

784.2672 

.3 

60.63274   292.5530 

.5  !  80.11061 

510.7052 

.7 

99.58849 

789.2388 

A 

60.94690   29.V>!»25 

.6  80.42477 

514.7185 

.8 

99.90265 

794.2260 

.5 

61.26106   298.6477 

.7  80  73893 

518.7476 

.9 

100.2168 

799.2290 

.6  61.57522   301.7186 

.8   81  .05309 

522.7924 

32,0 

100.5310 

804.2477 

.7  61.88938   304.8052 

.9  81.36725 

526.8529 

.1 

100.8451 

809.2821 

.8  62.20353   307.9075 

26.0  81.68141 

530.9292 

.2 

101.1593 

814.3322 

.9  62.51769   311.0255 

.1   81.99557 

535.0211 

.3 

101.4734 

819.3980 

20.0  62.83185   314.1593 

.2  82.30973 

539.1287 

.4 

101.7876 

824.4796 

.1   63.14001   317.3087 

.3   82.62389 

543.2521 

.5 

102.1018 

829.5768 

.'2   63.46017   3:20.4739 

.4   82.93805 

5473911 

'  .6 

102.4159 

834.6898 

.3  63.77433   323.6547 

.5   83.25221 

551.5459 

.7 

102.7301 

839.8184 

.4  ;  64.08849  ,  326.8513 

.6   83.56636 

555.7163 

.8  103.0442 

844.9628 

.5  64.40265   330.0636 

.7  :  83.88052 

559.9025 

.9  103.3584 

850.1228 

.6  i  64.71681   333.2916 

.8   84.19468 

564.1044 

33.0  103.6726 

855.2986 

.7  I  65.03097   336.5353 

.9   84.50884 

568.3220 

.1  103.9867 

860.4901 

.8  65.34513   339.7947 

27.0  I  84.82300 

572.5553 

.2  !  104.3009 

865.6973 

.9 

65.65929   343.0698 

.1   85.13716 

576.8043 

.3  |  104.6150 

870.9202 

21.0 

65.97345   346.3606 

.2  '  85.45132 

581.0690 

.4  104.9292 

87S.1588 

.1 

66.28760   349.6671 

.3   85.76548 

585.3494 

.5  105.2434 

881.4131 

.2 

66.60176   352.9894 

.4   86.07964 

589.6455 

.6 

105.5575 

886.6831 

.3 

66.91592   356.3273 

.5   86.39380 

593.9574 

.7 

105.8717 

891  .9688 

.4 

67.23008   359.6809 

.6   86.70796 

598.2849 

.8  i  106.1858 

897.2703 

.5 

67.54424   363.0503 

.7 

87.02212 

602.6282 

.9  106.5000 

902.5874 

.6 

67.85840   366.4354 

.8 

87.33628 

606.9871 

34.0  106.8142 

907.9203 

.7 

68.17256 

369.8361 

.9 

87.65044 

611.3618 

.1  107.1283 

913.2688 

.8 

68.48672   373.2526 

28.0 

87.96459   615.7522 

.2 

107.4425 

918.6331 

.9 

68,80088   376.6848 

.1   88.27875   620.1582 

.3 

107.7566 

924.0131 

22.0 

69.11504 

380.1327 

.2   88.59291 

624.5800 

.4  108.0708 

929.4088 

.1 

69.42920 

383.5963 

.3   88.90707 

629.0175 

.5  108.3849 

934.8202 

.2 

69.74336 

387.0756 

.4   89.22123 

633.4707 

.6  108.6991 

940.2473 

.3 

70.05752 

390.5707 

.5   89.53539   637.9397 

7 

109.0133 

945.6901 

.4 

70.37168 

394.0814 

.6   89.84955 

642.4243 

&  }  109.3274 

951.1486 

.5 

70.68583 

397.6078 

.7  |  90.16371 

646.9246 

.9  ;  109.6416 

956.6228 

.6 

70.99999   401.1500 

.8 

90.47787   651.4407 

35.0 

109.9557 

962.1128 

.7 

71.31415   404.7078 

9 

90.79203 

655.9724 

.1 

110.2699 

967.6184 

.8 

71.62831   408.2814 

29.0 

91.10619 

660.5199 

.2 

110.5841 

973.1397 

.9 

71.94247   411.8707 

.1 

91.42035 

665.0830 

.3 

110.8982  j  978.6768 

23.0 

72.25663   415.4756 

.2 

91.73451 

669.6619 

.4 

111.2124   984.22% 

.1 

72.57079   419.0963 

.3  92.04866   674.2565 

.5 

111.5265 

989.7980 

.2 

72.88495   422.7327 

.4  92.36282  1  678.8668 

.6 

111.8407 

995.3822 

.3 

73.19911   426.3848 

.5  92.67698   683.4928 

.7 

112.1549 

1000.9821 

.4 

73.51327  i  430.0526 

.6  92.99114   688.1345 

.8 

112.4690 

1006.5977 

.5 

73.82743   433.7361 

.7  93.30530 

692.7919 

.9 

112.7832 

1012.2290 

.6 

74.14159  i  437.4354 

.8  93.61946 

697.4650 

36.0 

113.0973 

1017.8760 

.7 

74.45575  j  441.1503 

.9  1  93.93362 

702.1538 

.1 

113.4115 

1023.5387 

.8 

74.76991   444.8809 

30.0  94.24778 

706.8583 

.2 

113.7257 

1029.2172 

.9 

75.08406   448.6273 

.1 

94.56194 

711.5786 

.3 

114.0398 

1034.9113 

24.0 

75.39822 

452.3893 

.2 

94.87610 

716.3145 

.4 

114.3540 

1040.6212 

.1 

75.71238 

456.1671 

.3 

95.19026 

721.0662 

.5 

114.6681 

1046.3467 

.2 

76.02654 

459.9606 

.4 

95.50442 

725.8336 

.6 

114.9823 

1052.0880 

.3 

76.34070 

463.7698 

.5 

95.81858 

730.6166 

.7 

115.2965 

1057.8449 

.4 

76.65486 

467.5947 

.6 

96.13274   735.4154 

.8 

115.6106 

1063.6176 

.5 

76.96902 

471.4352 

.7 

96.44689   740.2299 

.9 

115.9248 

1069.4060 

.6 

77.28318 

475.2916 

.8 

96.76105   745.0601 

37.0 

116.2389 

1075.2101 

.7 

77.59734 

479.1636 

.9 

97.07521  :  749.9060 

.1 

116.5531 

1081.0299 

.8 

77.91150 

483.0513 

31.0 

97.38937   754.7676 

.2 

116.8672 

1086.8654 

174  TABLE  NO.  72— CON. 

From  Trautwine's  "Civil  Engineer's  Pocket  Book." 

CIRCLES. 

TABLE  2  OF  CIRCL,ES-(Continued). 
Diameters  in  units  and  tenths. 


Dia. 

Circumf. 

Area. 

Dia. 

Circumf. 

Area. 

Dia. 

Circumf. 

Area. 

37.3 

117.1814 

1092.7166 

43.5 

136.6593 

1486.1697 

49.7 

156.1372 

1940.0041 

.4 

117.4956 

1098.5835 

.6 

136.9734 

1493.0105 

.8 

156.4513 

1947.8189 

.5 

117.8097 

1104.4662 

.7 

137.2876 

1499.8670 

.9 

156.7655 

1955.6493 

.6 

118.1239 

1110.3645 

.8 

137.6018 

1506.7393 

50.0 

157.0796 

1963.4954 

.7 

118.4380 

1116.2786 

.9 

137.9159 

1513.6272 

.1 

157.3938 

1971.3572 

.8 

118.7522 

1122.2083 

44.0 

138.2301 

1520.5308 

.2 

157.7080 

1979.2348 

.9 

119.0664 

1128.1538 

.1 

138.5442 

1527.4502 

.3 

158.0221 

1987.1280 

38.0 

119.3805 

1134.1149 

.2 

138.8584 

1534.3853 

.4 

158.3363 

1995.0370 

.1 

119.6947 

1140.0918 

.3 

139.1726 

1541.3360 

.5 

158.6504 

2002.9617 

.2 

120.0088 

1146.0'844 

.4 

139.4867 

1548.3025 

.6 

158.9646 

2010.9020 

.3 

120.3230 

1152.0927 

.5 

139.8009 

1555.2847 

.7 

159.2787 

2018.8581 

.4 

120.6372 

1158.1167 

.6 

140.1150 

1562.2826 

.8 

159.5929 

2026.8299 

.5 

120.9513 

1164.1564 

.7 

140.4292 

1569.2962 

.9 

159.9071 

2034.8174 

.6 

121.2655 

1170.2118 

.8 

140.7434 

1576.3255 

51.0 

160.2212 

2042.8206 

.7 

121.5796 

1176.2830 

.9 

141.0575 

1583.3706 

.1 

160.5354 

2050.8395 

.8 

121.8938 

1182.3698 

45.0  141.3717 

1590.4313 

.2 

160.8495 

2058.8742 

.9 

122.2080 

1188.4724 

.1  141.6858 

1597.5077 

.3 

161.1637 

2066.9245 

39.0 

122.5221 

1194.5906 

.2  142.0000 

1604.5999 

.4 

161.4779 

2074.9905 

.1 

122.8363 

1200.7246 

.3 

142.3141 

1611.7077 

.5 

161.7920 

2083.0723 

.2 

123.1504 

1206.8742 

.4 

142.6283 

1618.8313 

.6 

162.1062 

2091.1697 

.3 

123.4646 

1213.0396 

.5  142.9425 

1625.9705 

.7 

162.4203 

2099.2829 

.4 

123.7788 

1219.2207 

.6 

143.2566 

1633.1255 

.8 

162.7345 

2107.4118 

.5. 

124.0929 

1225.4175 

.7 

143.5708 

1640.2962 

.9 

163.0487 

2115.5563 

.6]  124.4071 

1231.6300 

g 

143.8849 

1647.4826 

52.0 

163.3628 

2123.7166 

.7  124.7212 

1237.8582 

!9 

144.1991 

1654.6847 

.1 

163.6770 

2131.8926 

.8 

125.0354 

1244.1021 

46.0 

144.5133 

1661.9025 

.2 

163.9911 

2140.0843 

.9 

125.3495 

1250.3617 

.1 

144.8274 

1669.1360 

.3 

164.3053 

2148.2917 

40.0 

125.6637 

1256.6371 

.2 

145.1416 

1676.3853 

.4 

164.6195  i  2156.5149 

.1   125.9779 

1262.9281 

.3 

145.4557 

1683.6502 

.5 

164.9336 

2164.7537 

.2  i  126.2920 

1269.2348 

.4 

145.7699 

1690.9308 

.6 

165.2478 

2173.0082 

.3 

126.6062 

1275.5573 

.5 

146.0841 

1698.2272 

.7 

165.5619  1  2181.2785 

.4 

126.9203 

1281.8955 

.6 

146.3982 

1705.5392 

.8 

165.8761  1  2189.5644 

.5 

127.2345 

1288.2493 

.7  146.7124 

1712.8670 

.9 

166.1903  !  2197.8661 

.6 

127.5487 

1294.6189 

.8 

147.0265 

1720.2105 

53.0 

166.5044  2206.1834 

.7 

127.8628 

1301.0042 

.9 

147.3407 

1727.5697 

.1 

166.8186  2214.5165 

.8 

128.1770 

1307.4052 

47.0 

147.6549 

1734.9445 

.2 

167.1327  2222.8653 

.9 

128.4911 

1313.8219 

.1 

147.9690 

1742.3351 

.3 

167.4469  2231.2298 

41.0 

128.8053 

1320.2543 

2 

148.2832 

1749.7414 

.4 

167.7610 

2239.6100 

.1 

129.1195 

1326.7024 

.3 

148.5973 

1757.1635 

.5 

168.0752 

2248.0059 

.2 

129.4336 

1333.1663 

.4 

148.9115 

1764.6012 

.6 

168.3894 

2256.4175 

.3 

129.7478 

1339.6458 

.5 

149.2257 

1772.0546 

.7 

168.7035 

2264.8448 

.4 

130.0619 

1346.1410 

.6 

149.5398 

1779.5237 

.8 

169.0177 

2273.2879 

.5 

130.3761 

1352.6520 

.7 

149.8540 

1787.0086 

.9 

169.3318 

2281.7466 

.6 

130.6903 

1359.1786 

.8 

150.1681 

1794.5091 

54.0 

169.6460 

2290.2210 

.7 

131.0044 

1365.7210 

.9 

150.4823 

1802.0254 

.1 

169.9602 

2298.7112 

.8 

131.3186 

1372.2791 

48.0 

150.7964 

1809.5574 

.2  ;  170.2743 

2307.2171 

.9 

131.6327 

1378.8529 

.1 

151.1106 

1817.1050 

.3  i  170.5885 

2315.7386 

42.0 

131.9469 

1385.4424 

.2 

151.4248 

1824.6684 

.4  !  170.9026 

2324.2759 

.1 

132.2611 

1392.0476 

.3 

151.7389 

1832.2475 

.5  171.2168 

2332.8289 

.2 

132.5752 

1398.6685 

.4 

152.0531 

1839.8423 

.6  171.5310 

2341.3976 

.3 

132.8894 

1405.3051 

.5 

152.3672 

1847.4528 

.7  I  171.8451 

2349.9820 

.4 

133.2035 

1411.9574 

.6 

152.6814 

1855.0790 

.8  j  172.1593 

2358.5821 

.5  !  133.5177 

1418.6254 

.7 

152.9956 

1862.7210 

.9  1  172.4734 

2367.1979 

.6  133.8318 

1425.3092 

.8 

153.3097 

1870.3786 

56.0  1  172.7876 

2375.8294 

.7 

134.1460 

1432.0086 

.9 

153.6239 

1878.0519 

.1 

173.1018 

2384.4767 

.8 

134.4602 

1438.7238 

49.0 

153.9380 

1885.7410 

!2 

173.4159 

2393.13% 

.9 

134.7743 

1445.4546 

.1 

154.2522 

1893.4457 

.3 

173.7301 

2401.8183 

43.0 

135.0885 

1452.2012 

.2 

154.5664 

1901.1662 

.4 

174.0442 

2410.5126 

.1 

135.4026 

1458.9635 

.3 

154.8805 

1908.9024 

.5 

174.3584 

2419.2227 

.2 

135.7168 

1465.7415 

.4 

155.1947 

1916.6543 

.6 

174.6726 

2427.9485 

.3 

136.0310 

1472.5352 

.5 

155.5088 

1924.4218 

.7 

174.9867 

2436.6899 

.4 

136.3451 

1479.3446 

.6 

155.8230 

1932.2051 

.8 

175.3009 

2445.4471 

TABLE  NO.  72— CON.  175 

From  Trautwi  II<**M  "Civil  Engineer***  Poeket  Book." 

CIRCLES. 

TABLE  2  OF   CIRCLES— (Continued). 
Diameters  in  units  and  tenths. 


Hia.  I  Hrcumf. 

Area. 

Dia. 

Circumf. 

Area. 

Dia. 

Circumf. 

Area. 


56.9  1  75.0150 

2454.2200 

6-2.1 

195.0929 

3028.8173 

68.3 

214.5708 

3663.7960 

66.0  175.9292 

2403.0086 

.2 

195.4071 

3038.5798 

.4 

214.8849 

3674.5324 

.1  1  76.2433 

2471.  MM 

.3 

195.7212 

3048.3580 

.5 

215.1991 

3685.2845 

.2   76.5575 

2480.0330 

.4 

196.0354  3058.1520 

.6 

215.5133 

3696.0523 

.3   76.8717 

2489.4687 

.5 

196.3495  3067.9616 

.7 

215.8274 

3706.8359 

A   77.1858 

2498.3201 

.6 

196.6637  3077.7869 

.8 

216.1416 

3717.6351 

.5   77.5000 

2507.1873 

.7 

190.9779  3087.6279 

.9 

216.4557 

3728.4500 

.6   77.8141 

2516.0701 

.8 

197.2920  I  3097.4847 

69.0 

216.7699 

3739.2807 

.7   78.1283 

2524.9687 

.9 

197.0062  3107.3571 

.1 

217.0841 

3750.1270 

.8   78.4425 

2533.8830 

63.0 

197.9203  3117.2453 

.2 

217.3982 

3760.9891 

.9   78.7560 

2542.8129 

.1 

198.2345  i  3127.1492 

.3 

217.7124 

3771.8668 

67.0   79.0708 

2551.7586 

.2 

198.5487 

3137.0688 

.4 

218.0265 

3782.7603 

.1   179.3849 

2560.7200 

.3 

198.8628 

3147.0040 

.5 

218.3407 

3793.6695 

.2   179.0991 

2569.6971 

.4 

199.1770 

3156.9550 

.6 

218.6548 

3804.5944 

.3  180.0133 

2578.6899 

.5 

199.4911 

3166.9217 

.7 

218.9690 

3815.5350 

.4  '  180.3274 

2587.6985 

.6 

199.8053 

3176.9042 

.8  219.2832 

3826.4913 

.5   180.6416 

2596.7227 

.7 

200.1195 

3186.9023 

.9  219.5973 

3837.4633 

.6   180.9557 

2605.7626 

.8 

200.4336 

3196.9161 

70.0 

219.9115 

3848.4510 

.7   181.2699 

2614.8183 

.9 

200.7478 

3206.9456 

.1 

220.2256 

3859.4544 

.8  181.5841 

2623.8896 

64.0 

201.0619 

3216.9909 

.2 

220.5398 

3870.4736 

.9  181.8982 

2632.9767 

.1 

201.3761 

3227.0518 

.3 

220.8540 

3881.5084 

68.0  182.2124 

2642.0794 

.2 

201.6902  3237.1285 

.4 

221.1681 

3892.5590 

.1  182.5265 

2651.1979 

.3 

202.0044 

3247.2209 

.5 

221.4823  i 

3903.6252 

.2   182.8407  ! 

2660.3321 

.4 

202.3186 

3257.3289 

.6 

221.7964 

3914.7072 

.3   183.1549 

2669.4820 

.5 

202.6327  3267.4527 

.7 

222.1106  ; 

3925.8049 

.4   183.4690 

2678.6476 

.6 

202.9469 

3277.5922 

.8 

222.4248 

3936.9182 

.5  183.7832 

2687.8289 

.7 

203.2610 

3287.7474 

.9 

222.7389  i 

3948.0473 

.6  184.0973 

2697.0259 

.8 

203.5752 

3297.9183 

71.0  223.0531 

3959.1921 

.7  184.4115 

2706.2386 

.9 

203.8894 

3308.1049 

.1  223.3672  ; 

3970.3526 

.8  184.7256 

2715.4670 

66.0 

204.2035  3318.3072 

.2  223.6814 

3981.5289 

.9  185.0398 

2724.7112 

.1 

204.5177  3328.5253 

.3  223.9956 

3992.7208 

69.0  185.3540 

2733.9710 

.2 

204.8318 

3338.7590 

.4  224.3097 

4003.9284 

.1   185.6681 

2743.2466 

.3 

205.1460  3349.0085 

.5  224.6239 

4015.1518 

.2  185.9823 

2752.5378 

.4 

205.4602  3359.2736 

.6  224.9380 

4026.3908 

.3  186.2964 

2761.8448 

.5 

205.7743  3369.5545 

.7 

225.2522 

4037.0456 

.4   186.6106 

2771.1675 

.6 

206.0885  3379.8510 

.8 

225.5664  ! 

4048.9160 

.5  I  186.9248 

2780.5058 

.7 

206.4026  3390.1633 

.9 

225.8805 

4060.2022 

.6  187.2389 

2789.8599 

.8 

2067168 

3400.4913 

72.0  226.1947  ! 

4071.5041 

.7  187.5531 

2799.2297 

.9 

207.0310 

3410.8350 

.1  226.5088 

4082.8217 

.8  '  187.8672 

2808.6152 

66.0 

207.3451  3421.1944 

.2  i  226.8230  ; 

4094.1550 

.9  188.1814 

2818.0165 

.1 

207.6593  3431.5695 

.3  1  227.1371  1 

4105.5040 

60.0  188.4956 

2827.4334 

.2 

207.9734  3441.  9603 

.4  227.4513  ' 

4116.8687 

.1  188.8097 

2836.8660 

.3 

208.2876  3452.3669 

.5  i  227.7655  ! 

4128.2491 

.2  189.1239 

2846.3144 

.4 

208.6018  3462.7891 

.6  ,  228.07%  i 

4139.6452 

.3  189.4380 

2855.7784 

.5 

208.9159 

3473.2270 

.7  228.3938  i 

4151.0571 

.4  189.7522 

2865.2582 

.61 

209.2301 

3483.6807 

.8  228.7079  j 

4162.4846 

.5  190.0664  , 

2874.7536 

.7  ! 

209.5442 

3494.1500 

.9  229.0221  j 

4173.9279 

.6  ,  190.3805 

2884.2648 

.8 

209.8584  3504.6351 

73.0  229.3363  > 

4185.3868 

.7  190.6947 

2893.7917 

.9 

210.1725  3515.1359 

.1  1  229.6504  i 

4196.8615 

.8  191.0088 

2903.3343 

67.0 

210.4867  £525.6524 

.2  229.9046  i 

4208.3519 

.9  191.3230 

2912.8926 

.1 

210.8009  3536.1845 

.3  230.2787  i 

4219.8579 

61.0  191.6372 

2922.4666 

.2 

211.1150  i  3546.7324 

.4 

230.5929  ! 

4231.3797 

.1  191.9513 

2932.0563 

.3 

211.4292  3557.2960 

.5 

230.9071 

4242.9172 

.2  192.2655 

2941.6617 

.4 

211.7433  3567.8754 

.6 

231.2212  j 

4254.4704 

.3   192.57% 

2951.2828 

.5 

212.0575  3578.4704 

.7 

231.5354  1 

4266.0394 

.4   192.8938 

2960.9197 

.6 

212.3717   3589.0811 

.8 

231.8495  ] 

4277.6240 

.5   193.2079  ' 

2970.5722 

.7 

212.6858   3599.7075 

.9 

232.1637 

4289.2243 

.6  193.5221 

2980.2405 

.8 

213.0000   3010.3497 

74.0 

232.4779 

4300.8403 

.7  193.8363 

2989.9244 

.9 

213.3141  !  3621.0075 

.1 

232.7920  i 

4312.4721 

.8  194.1504 

2999.6241 

68.0 

213.6283  '  3631.6811 

233.1062  ' 

4324.1195 

.9   194.4646 

3009.3395 

.1 

213.9425   3642.3704 

i3  1  233.4203  1  4335.7827 

fl?0   194.77*7 

wn  9.0705 

.2 

214.2566   3653.0754 

.4  i  233.7345  j  4347.4616 

176  TABLE  NO.  72— CON. 

From  Traut wine's  " Civil  F,un  inker's  Pocket  Hook 

CIRCLES. 

TABLE  2   OF   CIRCLES— (Continued). 
Diameters  in  units  and  tenths. 


Dia. 

Circumf. 

Area. 

Dia. 

Circumf. 

Area. 

Dia. 

Circumf. 

Area. 

74.5 

234.0487 

4359.1562 

80.7 

253.5265 

5114.8977 

86.9 

273.0044 

5931.0206 

.6 

234.3628 

4370.8664 

.8 

253.8407 

5127.5819 

87.0 

273.3186 

5944.6787 

7 

234.6770 

4382.5924 

.9 

254.1548 

5140.2818 

.1 

273.6327 

5958.3525 

*8 

284.9911 

439-1.3341 

81.0 

254.4690 

5152.9974 

2 

273.9469 

5972.0420 

.9 

235.3053 

4406.0916 

.1 

254.7832 

5165.7287 

.3 

274.2610 

5985.7472 

75.0 

235.6194 

4417.8647 

.2 

255.0973 

5178.4757 

'A 

274.5752 

5999.4681 

.1 

235.9336 

4429.6535 

.3 

255.4115 

5191.2384 

.5 

274.8894 

6013.2047 

.2 

236.2478 

4441.4580 

.4 

255.7256 

5204.0168 

.6 

275.2035 

6026.9570 

.3 

236.5619  4453.2783 

.5 

256.0398 

5216.8110 

.7 

275.5177 

6040.7250 

.4 

236.8761  j  4465.1142 

.6 

256.3540 

5229.6208 

.8 

275.8318 

6054.5088 

.5 

237.1902  4476.9659 

.7 

256.6681 

5242.4463 

.9 

276.1460 

6068.3082 

.6 

237.5044 

4488  8332 

.8 

256.9823 

5255.2876 

88.0 

276.4602 

6082.1234 

.7 

237.8186 

4500.7163 

.9 

257.2964 

5268.1446 

.1 

276.7743 

6095.9542 

.8 

238.1327 

4512.6151 

82.0 

257.6106 

5281.0173 

.2 

277.0885 

6109.8008 

.9 

238.4469 

4524.5296 

.1 

257.9248 

5293.9056 

.3 

277.4026 

6123.6631 

76.0  238.7610 

4536.4598 

o 

258.2389 

5306.8097 

.4 

277.7168 

6137.5411 

.1  I  239.0752 

4548.4057 

!a 

258.5531 

5319.7295 

.5 

278.0309 

6151.4348 

.2  !  239.3894 

J  560.3673 

.4 

258.8672 

5332.6650 

.6 

278.3451 

6165.3442 

.3  239.7035 

4572.3446 

.5 

259.1814 

5345.6162 

7 

278.6593 

6179.2693 

.4  240.0177 

4584.3377 

.6 

259.4956 

5358.5832 

'.% 

278.9734 

6193.2101 

.5  240.3318 

4596.3464 

.7 

259.8097 

5371  .5658 

9 

279.2876 

6207.1666 

.6  240  6400 

4608.3708 

.8 

260.1239 

5384.5641 

89.0 

279.6017 

6221.1389 

.7  240.9602 

4620.4110 

.9 

260.4380 

5397.5782 

.1 

279.9159 

6235.1268 

.8  241.2743 

4632.4669 

830 

260.7522 

5410.6079 

.2 

280.2301 

6249.1304 

.9  ,  241.5885  ;  4614  5384 

.1  261.0663 

5423.6534 

.3 

280.5442  6263.1498 

77.0  241.9026  4656.6257 

.2  261.3805 

5436.7146 

.4 

280.8584  6277.1849 

.1 

242.2168  i  4668.7287 

.3  261.6947 

5449.7915 

£, 

281.1725  6291  2356 

.2 

242.5310 

4680.8474 

.4  262.0088 

5462.8840 

!« 

281.4867  6305.3021 

.3 

242.8451 

4692.9818 

.5  262.3230 

5475.9923 

.7 

281.8009  6319.3843 

.4 

243.1593 

4705.1319 

.6  262.6371 

5489.1163 

.8 

282.1150  6333.4822 

.5 

243.4734 

4717.2977 

.7  262.9513 

5502.2561 

.9 

282.4292  6347.5958 

.6 

243.7876 

4729.4792 

.8  263.2655 

5515.4115 

90.0 

282.7433  6361.7251 

.7 

244.1017 

4741.6765 

.9  263.5796 

5528.5826 

.1 

283.0575  6375.8701 

.8 

244.4159 

4753.8894 

84.0  263.8938 

5541.7694 

.2 

283.3717  6390.0309 

.9 

244.7301 

4766.1181 

.1 

264.2079 

5554.9720 

.3 

283.6858  '  6404.2073 

78.0 

245.0442 

4778.3624 

.2  j  264.5221 

5568.1902 

.4 

284.0000  6418.3995 

.1 

245.3584 

4790.6225 

.3 

264.8363 

5581.4242 

.5 

284.3141   6432.6073 

.2 

245.6725 

4802.8983 

.4 

265.1504 

£594.6739 

.6 

284.6283  6446.8309 

.3 

245.9867 

4815.1897 

.5  265.4646 

5607.9392 

.7 

284.9425  6461.0701 

A 

246.3009 

4827.4969 

.6  265.7787 

5621.2203 

.8 

285.2566  6475.3251 

.5 

246.6150 

4839.8198 

.7  266.0929 

5634.5171 

.9 

285.5708  6489.5958 

.6 

246.9292 

4852.1584 

.8  266.4071 

5647.8296 

91.0 

285.8849  6503.8822 

,7 

IJ47.243? 

4864.5128 

.9  !  266.7212 

5661.1578 

.1 

286.1991   6518.1843 

.8 

247.5575  |  l8/tj.3828 

85.0;  2670354 

5674.5017 

.2 

286.5133  6532.5021 

.9 

247.8717  .  4889.2685 

.1  !  267  3495 

5687.8614 

.3 

286.8274  6546.8356 

79.0 

248.185S  •  4901  .669£ 

.2  267  6637 

5701.2367 

.4 

287.1416  6561.1848 

.1 

248.5000 

4914.087-.: 

.3 

267  9779 

5714.6277 

.5 

287.4557  !  6575.5498 

.2 

248.8141 

4926.5199 

.4 

268.2920 

5728.0345 

.6 

287.7699  6589.9304 

.3 

249.1283 

4938.9685 

.5 

268.6062 

5741.4569 

.7 

288.0840  6604.3268 

.4 

249.4425 

4951.4328 

.6 

268.9203 

5754.8951 

.8 

288.3982  6618.7388 

.5 

249.7566 

4963.9127 

.7 

269.2345 

5768.3490 

.9 

288.7124  6633.1666 

.6 

250.0738  4976.4084 

.8 

269.5486 

5781.8185 

92.0 

289.0265  6647.6101 

.7 

250.3843  ';  4988.H9S 

.9  269.8628 

5795.3038 

.1 

289.3407  6662.0692 

.8 

250.6991  50Ci/.-469 

86.0  !  279.1770 

5808.8048 

.2 

289.6548  6676.5441 

9 

251.0133  5013.9897 

.1  !  2'*  0.4911 

5822.3215 

.3 

289.9690  6691.0347 

80.0 

251.3274  £026.5482 

.2  ;  270.8053  5835.8539 

*  .4 

290.2832  6705.5410 

.1 

251.6416  5039.1225 

.3  271.1194 

5849.4020 

.5 

290.5973  6720.0630 

.2 

251.9557  5051.7121 

.4  271.43H6 

5862.9659 

.6 

290.9115  i  6734.6008 

.3 

252.11699  5064.3180 

.5  271.7478 

5876.5454 

.7 

291.2256  6749.1542 

.4 

252.5840  i  5076.9894 

.6  '  272.0619 

5890.1407 

.8 

291.5398  6763.7233 

.5 

252.8982  ;  5089.5764 

.7  272.3761 

5903.7516 

9 

291.8540  6778.3082 

.6 

253.2124  i  5102.2292 

.8  ''  272.6902 

5917.3783 

9s!o 

292.1681  ;  6792.9087 

TABLE  NO.  72— COX.  177 

From  Trautwine's  *•«  ivil   i:n^iiio<>r*s  Pocket  Book." 

CIRCLES. 

TABLE  2  OF  CIRCLES— (Continued). 
Diameters  in  units  and  tenths. 


Dia. 

Circumf. 

Area. 

Dia.  |  Circumf. 

Area. 

Dia. 

Circumf. 

Area. 

93.1 

292.4823 

6807.5250 

955 

300.0221 

7163.0276 

97.8 

307.2478 

7512.2078 

.2 

292.7964 

6822.1569 

.6 

300.3363 

7178.0366 

.9 

307.5619 

7527.5780 

.3 

293.1106 

6836.8046 

.7   300.6504 

7193.0612 

98.0 

307.8761 

7542.9640 

.4 

293.4248 

6851.4680 

.8   300.9646 

7208.1016 

.1 

308.1902 

7558.3656 

.5 

293.7389 

6866.1471 

.9   301.2787  7223.1577 

.2 

308.5044 

7573.7830 

6 

294.0-')31 

6880.8419 

96.0 

301.5929 

7238.2295 

.3 

308.8186 

7589.2161 

.7 

294.3672 

6895.5524 

.1 

301.9071  1  7253.3170 

.4 

309.1327 

7604.6648 

.8 

294.6814 

6910.2786 

.2 

302.2212  7268.4202 

.5 

309.4469 

7620.1293 

.9  !  294.9956 

6925.0205 

.3  j  302.5354 

7283.5391 

.6 

309.7610 

7635.6095 

94.0 

295.3097 

6939.7782 

.4   302.8495 

7298.6737 

.7 

310.0752 

7651.1054 

.1 

295.6239 

0954.5515 

.5   303.1637 

7313.8240 

.8 

310.3894 

7666.6170 

.2 

295.9380 

6969.3406 

.6   303.4779 

7328.9901 

.9 

310.7035 

7682.1444 

.3 

296.2522 

6984.1453 

.7   303.7920 

7344.1718 

99.0 

311.0177 

7697.6874 

.4 

296.5663 

6998.9658 

.  .8   304.1062 

7359.3693 

.1 

311.3318 

7713.2461 

.5 

29(5.8805 

7013.8019 

.9   304.4203 

7374.5824 

.2 

311.6460 

7728.8206 

.6 

297.1947 

7028.6538 

97.0   304.7345 

7389.8113 

.3 

311.9602 

7744.4107 

.7 

297.5088 

7043.5214 

.1   305.0486 

7405.0559 

.4 

312.2743 

7760.0166 

.8 

297.8230 

7058.4047 

.2   305.3628 

7420.3162 

.5 

312.5885 

7775.6382 

.9 

298.1371 

7073.3037 

.3   305.6770 

7435.5922 

.6 

312.9026 

7791.2754 

95.0 

298.4513 

7088.2184 

.4 

305.9911 

7450.8839 

.7 

313.2168 

7806.9284 

.1 

298.7655 

7103.1488 

.5 

306.3053 

7466.1913 

.8 

313.5309 

7822.5971 

.2 

299.0796 

7118.0950 

.6 

306.6194 

7481.5144 

.9 

313.8451 

7838.2815 

.3 

299.3938 

7133.0568 

.7 

306.9336 

7496.8532 

100.0 

314.1593 

7853.9816 

.4 

299.7079 

7148.0343 

Circumferences  when  the  diameter  has  more  than  one 
place  of  decimals. 


Diam. 

Circ. 

Diam. 

Circ. 

Diam. 

Circ. 

Diam. 

Circ. 

Diam. 

Circ. 

.1 

.314159 

.01 

.031416 

.001 

.003142 

.0001 

.000314 

.00001 

.000031 

.2 

.628319 

.02 

.062832 

.002 

.006283 

.0002 

.000628 

.00002 

.000063 

!   .3 

.942478 

.03 

.094248 

.003 

.009425 

.0003 

.000942 

.00003 

.000094 

.1 

1.256637 

.04 

.125664 

.004 

.012566 

.0004 

.001257 

.00004 

.000126 

.5 

1  570796. 

.05 

.157080 

.005 

.015708 

.0005 

.001571 

.00005 

.000157 

.6 

1.884956 

.06 

.188496 

.006 

.018850 

.0006 

.001885 

.00006 

.000188 

.7 

2.199115 

1  .07 

.219911 

.007 

.021991 

.0007 

.002199 

.00007 

.000220 

.8 

2.513274 

.08 

.251327 

.008   .025133 

.0008 

.002513 

.00008 

.000251 

.9 

2.827433 

.09   .282743 

.009 

.028274 

.0009 

.002827 

.00009 

.000283 

Examples. 


Diameter  =  3.12699 
Circumference  = 

Circ  for  dia  of        3.1 

.02 

"  .006 

"  .0009 

"  .00009 


Sum  of 
=  9.738937 

Circumfce  = 
Diameter  = 

Dia  for  circ  of 

M 

9.823729 
9.738937  = 

Sum  of 
3.1 

.02 
.006 
.0009 
.00009 

=     .062832 
=     .018850 

.084792 
.062832  = 

=     .000283 

.021960 
.018850  = 

9.823729 

.003110 
.002827  = 
.000283 
.000283  = 

178  TABLE  KG.  73. 

From  Trawtwine*s  "C'ivil  Engineer**  Pocket  Book." 

CIRCLES. 

TABLE  3  OF   CIRCLES. 
Dia  ins  in  units  and  twelfths ;  as  in  feet  and  inches. 


Dia. 

Circumf. 

Area. 

Dia.  Circumf.j  Area. 

Dia. 

C'ircumf.   Area. 

Ft.In. 

Feet. 

Sq.  ft. 

Ft.In.   Feet.     Sq.  ft. 

Ft  In. 

Feet.   :   Sq.  ft. 

5  0  15.70796  19.63495 

10  0 

31.41593   78.53982 

0  1 

.261799 

.005454 

1  15.96976  20.29491 

1 

31.67773   79.85427 

2 

.523599 

.021817 

2  16.23156 

20.96577 

2  31.93953   81.17963 

3 

.785398 

.049087 

3  16.49336  21.64754 

3  32.20132   82.515-S'J 

4 

1.047198  i   .087266 

4  1(5.75516 

22.34021 

4  32.46312  :  83.86307 

5 

1.308997   .136354 

5 

17.01696 

23.04380 

5  |  32.72492   85.22115 

6 

1.570796   .196350 

6 

17.27876 

23.75829 

6  32.98672   86.59015 

7 

1.832596   .267254 

7 

17.54056 

24.48370 

7  33.24852  :  87.97005 

8 

2.094395 

.349066 

8 

17.80236 

25.22001 

8  33.51032   89.36086 

9 

2.356195 

•441786 

9 

18.06416 

25.96723 

9  83.77212 

90.76258 

10 

2.617994 

.545415 

10 

18.32596 

26.72535 

10 

34.03392 

92.17520 

11 

2.879793 

.659953 

11 

18.58776 

27.49439- 

11 

34.29572   93.59874 

1  0 

3.14159 

.785398 

6  0 

18.84956 

28.27433 

11  0 

34.55752  ;  95.03318 

1 

3.40339 

.921752 

1 

19.11136 

29.06519 

1 

34.81932  i  96.47853 

2 

3.66519 

1.06901 

2 

19.37315 

29.86695 

2 

35.08112  !  97.im7J 

3 

3.92699 

1.22718 

3 

19.63495 

30.67962 

3  1  35.34292  !  99.40196 

4 

4.18879 

1.39626 

4 

19.89675 

31.50319 

4  35.60472  j  100.8800 

5 

4.45059 

1.57625 

5 

20.15855 

32.33768 

5  35.86652  '  102.3690 

6 

4.71239 

1.76715 

6 

20.42035 

33.18307 

6 

36.12832  !  103.8689 

7 

4.97419 

1.96895 

7 

20.68215 

34.03937 

7 

36.39011  105.3797 

8 

5.23599 

2.18166 

8 

20.94395 

34.90659 

8  36.65191  106.9014 

9 

5.49779 

2.40528 

9 

21.20575 

35.78470 

9  36.91371 

108.4340 

10 

5.75959 

2.63981 

10 

21.46755 

36.67373 

10  1  37.17551 

1(19.9776 

11 

6.02139 

2.88525 

11 

21.72935 

37.57367 

11  |  37.43731 

111.5320 

9  0 

6.28319 

3.14159 

7  0 

21.99115 

38.48451 

12  0  37.69911 

1  13.0973 

1 

6.54498 

3.40885 

1 

22.25295 

39.40626 

1  :  57.  96091 

114.6736 

2 

6.80678 

3.68701 

o 

22.51475 

40.33892 

2  '  3.S.22271 

116.2607 

3 

7.06858 

3.97608 

3 

22.77655 

41.28249 

3  '  38.48451 

117.8588 

4 

7.33038 

4.27606 

4 

23.03835 

42.23697 

4  38.74631 

119.467S 

5 

7.59218 

4.58694 

5 

23.30015 

\o  20235 

5  :ri9.00811 

121  0*77 

6 

7.85398 

4.90874 

6 

23.56194   '.4,  .7865 

6  39.26991 

122.71.  S5 

7 

8.11578 

5.24144 

7 

23.82374  45.16585 

7  39.53171 

124.3602 

8 

8.37758 

5.58505 

8 

24.08554 

46.16396 

8  39.79351 

126.0128 

9 

8.63938 

5.93957 

9 

24.34734 

47.17298 

9 

40.05531 

127.6763 

10 

8.90118 

6.30500 

10 

24.60914 

48.19290 

10 

40.31711 

129.3507 

11 

9.16298 

6.68134 

11 

24.87094 

49.22374 

11 

40.57891 

131.0360 

8  0 

9.42478 

7.06858 

8  0 

25.13274 

50.26548 

13  0 

40.84070 

132.7323 

1 

9.68658 

7.46674 

1 

25.39454 

51.31813 

1 

41.10250 

134.4394 

2 

9.94838 

7.87580 

2 

25.65634 

52.38169 

2 

41.36480 

136.1575 

3 

10.21018 

8.29577 

3 

25.91814 

53.45616 

3 

41.62610 

137.8865 

4 

10.47198 

8.72665 

4 

26.17994 

54.54154 

4 

41.88790 

139.6263 

5 

10.73377 

9.16843 

5 

26.44174 

55.63782 

5 

42.14970 

141.3771 

6 

10.99557 

9.62113 

6 

26.70354 

56.74502 

6 

42.41150 

143.1388 

7 

11.25737 

10.08473 

7 

26.96534 

57.86312 

7 

42.67330 

144.9114 

8 

11.51917 

10.55924 

8 

27.22714 

58.99213 

8 

42.93510 

146.6949 

9 

11.78097 

11.04466 

9 

27.48894 

60.13205 

9 

43.19690 

148.4893 

10 

12.04277 

11.54099 

10 

27.75074 

61.28287 

10 

43.45870 

150.2947 

11 

12.30457 

12.04823 

11 

28.01253 

62.44461 

11 

43.72050 

152.1109 

4  0 

12.56637 

12.56637 

9  0 

28.27433 

63.61725 

14  0 

43.98230 

153.9380 

1 

12.82817 

13.09542 

1 

28.53613 

64.80080 

1 

44.24410 

155.7761 

2 

13.08997 

13.63538 

2 

28.79793 

65.99526 

2 

44.50590 

157.6250 

3 

13.35177 

14.18625 

3 

29.05973 

67.20063 

3 

44.76770 

159.48411 

4 

13.61357 

14.74803 

4 

29.32153 

68.41691 

4 

45.02949 

161.3557 

5 

13.87537 

15.32072 

5 

29.58333 

69.64409 

5 

45.29129 

163.2374 

6 

14.13717 

15.90431 

6 

29.84513 

70.88218 

6 

45.55309 

165.1300 

7 

14.39897 

16.49882 

7 

30.10693 

72.13119 

7 

45.81489 

167.0335 

8 

14.66077 

17.10423 

8 

30.36873 

73.39110 

8 

46.07669 

168.9472 

9 

14.92257 

17.72055 

9 

30.63053 

74.66191 

9 

46.33849 

170.8732 

10 

15.18436 

18.34777 

10 

30.89233 

75.94364 

10 

46.60029 

172.8094 

11 

15.44616 

18.98591 

11 

31.15413 

77.23627 

11 

46.86209 

174.7565 

TABLE  NO.  73— CON. 
From  Traiitwine's  "Civil  Engineer's  Pocket  Book." 

CIRCLES. 


man 


TABLE  3  OF   CIRCLES— (Continued). 
in  units  and  twelfths;  as  in  feet  and  inches. 


Dia. 

Circumf. 

Area. 

Dia.  Circumf. 

Area. 

Dia. 

Circumf. 

Area. 

Ft.In. 

Feet. 

Sq.  ft. 

Ft.In.   Feet. 

Sq.  ft. 

Ft.In. 

Feet. 

Sq.  ft. 

15  0 

47.12389 

176.7146 

20  0  62.83185 

314.1593 

25  0 

78.53982 

490.8739 

1 

47.38569 

178.6835 

1  63.09365 

316.7827 

1 

78.80162 

494.1518 

2 

47.64749 

180.6634 

2  63.35545 

319.4171 

2 

79.06342 

497.4407 

3 

47.90929 

182.6542 

3  ;  63.61725 

322.0623 

3 

79.32521 

500.7404 

4 

48.17109 

184.6558 

4  !  63.87905 

324.7185 

4 

79.58701 

504.0511 

5 

48.43289 

186.6684 

5  64.14085 

327.3856 

5 

79.84881 

507.3727 

<1  48.69469 

188.6919 

6  64.40265 

330.0636 

6  80.11061 

510.7052 

7 

48.95649 

190.7263 

7  64.66445  |  332.7525 

7  80.37241 

514.0486 

1 

49.21828 

192.7716 

8  64.92625 

335.4523 

8  80.63421 

517.4029 

9 

49.48008 

194.8278 

9  65.18805 

338.1630 

9  80.89601 

520.7681 

10 

49.74188 

196.8950 

10  65.44985 

340.8846 

10  i  81.15781 

524.1442 

11 

50.00368 

198.9730 

11  65.71165 

343.6172 

11  81.41961 

527.5312 

16  0 

50.26548 

201.0619 

21  0  65.97345 

346.3606 

26  0  !  81.68141 

530.9292 

1 

50.52728 

203.1618 

1  66.23525 

349.1149 

1 

81.94321 

534.3380 

2 

50.78908 

205.2725 

2  66.49704 

351.8802 

2 

82.20501 

537.7578 

3 

51.05088 

207.3942 

3  66.75884 

354.6564 

0 

82.46681 

541.1884 

4 

51.31268 

209.5268 

4  67.02064 

357.4434 

4  82.72861 

544.6300 

5 

51.57448 

211.6703 

5  67.28244 

360.2414 

5  !  82.99041 

548.0825 

6 

51.83628 

213.8246 

6  67.54424 

363.0503 

6  !  83.25221 

551.5459 

7 

52.09808 

215.9899 

7  67.80604 

365.8701 

7  83.51400 

555.0202 

8 

52.35988 

218.1662 

8  68.06784 

368.7008 

8  83.77580 

558.5054 

9 

52.62168 

220.3533 

9  68.32964 

371.5424 

9  84.03760 

562.0015 

10 

52.88348 

222.5513 

10  68.59144 

374.3949 

10 

84.29940 

565.5085 

11 

53.14528 

224.7602 

11  68.85324 

377.2584 

11 

84.56120 

569.0264 

17  0 

53.40708 

226.9801 

22  0  69.11504. 

380.1327 

27  0 

84.82300 

572.5553 

1 

53.66887 

229.2108 

1  6937684 

383.0180 

1 

85.08480 

576.0950 

2 

53.93067 

231.4525 

2  69.63864 

385.9141 

2 

85.34660 

579.6457 

3 

54.19247 

233.7050 

3  69.90044 

388.8212 

3 

85.60840 

583.2072 

4 

54.45427 

235.96&5 

4  70.16224 

391.7392 

4 

85.87020 

586.7797 

5 

54.71607 

238.2429 

5  70.42404 

394.6680 

5 

86.13200 

590.3631 

6 

54.97787 

240.5282 

6  70.68583 

397.6078 

6 

86.39380 

593.9574 

7 

55.23967 

242.8244 

7  70.94763 

400.5585 

7 

86.65560 

597.5626 

8 

55.50147 

•  245.1315 

8  71.20943 

403.5201 

8 

86.91740 

601.1787 

9 

55.76327 

247.4495 

9  71.47123 

406.4926 

9  87.17920 

604.8057 

10 

56.02507 

249.7784 

10  71.73303 

409.4761 

10  87.44100 

608.4436 

11 

56.28687 

252.1183 

11  71.99483 

412.4704 

11  87.70279 

612.0924 

18  0 

56.54867 

254.4690 

23  0  72.25663 

415.4756 

28  0  87.96459 

615.7522 

1 

56.81047 

256.8307 

1  72.51843 

418.4918 

1  88.22639 

619.4228 

2 

57.07227 

259.2032 

2  72.78023 

421.5188 

2  88.48819 

623.1044 

3 

57.33407 

261.5867 

3  73.04203 

424.5568 

3  88.74999 

626.7968 

4 

57.59587 

263.9810 

4  73.30383 

427.6057 

4  89.01179 

630.5002 

5 

57.85766 

266.3863 

5  73.56563 

4306654 

5  89.27359 

634.2145 

6 

58.11946 

268.8025 

6  73.82743 

433.7361 

6  89.53539 

637.9397 

7 

58.38126 

271.2296 

7  74.08923 

436.8177 

7  89.79719 

641.6758 

8 

58.64306 

273.6676 

8  74.35103 

439.9102 

8  90.05899 

645.4228 

9 

58.90486 

276.1165 

9  74.61283 

443.0137 

9  90.32079 

649.1807 

10 

59.16666 

278.5764 

10  74.87462 

446.1280 

10  90.58259 

652.9495 

11 

59.42846 

281.0471 

11  75.13642 

449.2532 

11  ,  90.84439 

656.7292 

19  0 

59.69026 

283.5287 

24  0  75.39822 

452.3893 

29  0  91.10619 

660.5199 

1 

59.95206 

286.0213 

1  75.66002 

455.53^4 

1  :  91.36799 

664.3214 

2 

60.21386 

288.5247 

2  75.92182 

458.6943 

2  •  91.62979 

668.1339 

3 

60.47566 

291.0391 

3  76.18362 

461.8632 

3  :  91.89159 

671.9572 

4 

60.73746 

293.5644 

4  76.44542 

465.0430 

4  92.15338 

675.7915 

5 

60.99926 

296.1006 

5  76.70722 

468.2337 

5  ,  92.41518 

679.6367 

6 

61.26106 

298.6477 

6  76.96902 

471.4352 

6  92.67698 

683.492* 

7 

61.52286 

301.2056 

7  77.23082 

474.6477 

7  j  92.93878 

687.3591 

8 

61.78466 

303.7746 

8  77.49262 

477.8711 

8  93.20058 

691.2377 

9 

62.04645 

306.3544 

9  77.75442 

481.1055 

93.46238 

695.1263 

10 

62.30825 

308.9451 

10  78.01622 

484.3507 

10  L  93.72418 

699.026J 

11 

62.57005 

311.5467 

11  78.27802 

487.6068 

11 

93.98598 

702.9361 

180  TABLE  KO.  73-COSr. 

From  Trautwine's  "Civil  Engineer's  Pocket  Book." 

CIRCLES. 

TABLE  3  OF  CIRCIiES-(Continued). 
Dianm    in  units  and  twelfths;  as  in  feet  and  inches. 


Dia.  jcircumf. 

Area. 

Dia.  .Circumf. 

Area. 

Dia. 

Circumf. 

Area. 

Ft.  In. 

Feet. 

Sq.  ft. 

Ft.In 

Feet. 

Sq.  ft. 

Ft.In 

Feet. 

Sq.  ft. 

30  0 

94.24778 

706.8583 

35  0 

109.9557 

962.1128 

40  0 

125.6637 

1256.6371 

1 

94.50958 

710.7908 

1 

110.2175 

966.6997 

1 

125.9255 

1261.8785 

2 

94.77138 

714.7341 

2 

110.4793 

971.2975 

126.1873 

1267.1309 

3 

95.03318 

718.6884 

3 

110.7411 

975.9063 

B 

126.4491 

1272.3941 

4 

95.29498 

722.6536 

4 

111.0029 

980.5260 

4 

126.7109 

1277.6683 

5 

95.55678 

726.6297 

5 

111.2647 

985.1566 

i 

126.9727 

1282.9534 

6 

95.81858 

730.6166 

6 

111.5265 

989.7980 

e 

127.2345 

1288.2493 

7 

96.08038 

734.6145 

7 

111.7883 

994.4504 

7 

127.4963 

1293.5562 

8 

96.34217 

738.6233 

8 

112.0501 

999.1137 

8 

127.7561  I  1298.8740 

9 

96.60397  ,  742.6431 

9 

112.3119 

1003.7879 

9 

128.0199  1304.2027 

10 

96.86577 

746  6737 

10 

112.5737 

1008.4731 

10 

128.2817 

1309.5424 

11 

97.12757 

750.7152 

11 

112.8355 

1013.1601 

11 

128.5435 

1314.8929 

31  0 

97.38937 

754.7676 

36  0 

113.0973 

1017.8700 

41  0 

128.8053 

1320.2543 

1 

97.65117 

758.8310 

1 

113.3591 

1022.5939 

1 

129.0671 

1325.6267 

2 

97.91297 

.  762.9052 

2 

113.6209 

1027.3226 

2 

129.3289 

1331.0099 

3 

98.17477 

766.9904 

3 

113.8827 

1032.0623 

5 

129,5907 

1336.4041 

4 

98.43657 

771.0865 

4 

114.1445 

1036.8128 

4 

129.8525 

1341.8091 

5 

98.69837 

775.1934 

5 

114.4063 

1041.5743 

5 

130.1143 

1347.2251 

6 

98.96017 

779.3113 

6 

114.6681 

1046.3467 

6 

130.3761 

1352.6520 

7 

99.22197 

783.4401 

7 

114.9209 

1051.1300 

7 

130.6379 

1358.0898 

8 

99.48377 

787.5798 

8 

115.1917 

1055.9242 

8 

130.8997 

1363.5385 

9  99.74557 

791.7304 

9 

115.4535 

1060.7293 

9 

131.1615 

1368.9981 

10  100.0074 

795.8920 

10 

115.7153 

10G5.54-13 

10 

131.4233 

1374.4686 

11  i  100.2692 

800.0644 

11 

115.9771 

1070.3723 

11 

131.6851 

1379.9500 

82  0 

100.5310 

804.2477 

37  0 

116.2889 

1075.2101 

42  0 

131.9469 

1385.4424 

1 

100.7928 

808.4420 

1 

116.5007 

10S0.05S8 

1 

132.2087 

1390.9456 

2 

101.0546 

812.6471 

2 

116.7625 

1084.9185 

2 

132.4705 

1396.4598 

3  1101.3164 

816.8632 

3 

117.0243 

1089.7800 

3 

132.7323 

1401.9848 

4  1  101.5782 

821.0901 

4 

117.2861 

1094.6705 

4 

132.9941 

1407.5208 

5  1101.8400 

825.3280 

5 

117.5479 

1099.5629 

5 

133.2559 

1413.0676 

6  102.1018 

829  5768 

6 

117.8097 

1104.4662 

6 

133.5177 

1418.6254 

7  102.3636  ;  833.8365 

7 

118.0715 

1109.3804 

7 

133.7795 

1424.1941 

8  102.6254 

838.1071 

8 

118.3333 

1114.3055 

8 

134.0413 

1429.7737 

9  1102.8872 

842.3886 

9 

118.5951 

1119.2415 

9 

134.3031 

1435.3642 

10  1103.1490 

846.6810 

10 

]  18.8569' 

1124.1884 

10 

134.5649 

1440.9656 

11  103.4108 

850.9844 

11 

119.1187 

1129.1462 

11 

134.8267 

1446.5780 

33  0  ;  103  .6726 

855.2986 

38  0 

119.3805 

1134.1149 

43  0 

135.0885 

1452.2012 

1  :  103.9344 

859.6237 

1 

119.6423 

1139.0946 

1 

335.3503 

3457.8353 

2  ;  104.1962 

863.9598 

2 

li  9.9041 

1144.0851 

2 

135.6121 

1463.4804 

3  104.4580 

868.3068 

3 

r:0.1659 

1149.08C6 

3 

135.8739 

1469.1364 

4  ;104.7198 

872.6646 

4 

120.4277 

1154.0990 

4 

136.1357 

1474.8032 

5  i  104.9816 

877.0334 

5 

120.6895 

1159.1222 

5 

136.3975 

1480.4810 

6  105.2434 

881.4131 

6 

120.9513 

1164.1564 

6 

136.6593 

1486.1697 

7  1105.5052 

885.8037 

7 

121.213J 

1169.2015 

7 

136.9211 

1491.8693 

8  1105.7670 
9  1106.0288 

890.2052 
894.6176 

8 
9 

121.4749 
121.7367 

1174.2575 
1179.3244 

8 
9 

137.1829 
137.4447 

1497.5798 
1503.3012 

10 

106.2906 

899  0409 

10 

121.9985 

1184.4022 

10 

137.7065 

1509.0335 

11 

106.5524 

903.4751 

11 

122.2603 

1189.4910 

11 

137.9683 

1514.7767 

34  0 

106.8142 

907.9203 

39  0 

122.5221 

1194.5906 

44  0 

138.2301 

1520.5308 

1 

107.0759 

912.3763 

*1 

122.7839 

1199.7011 

1 

138.4919 

1526.2959 

2 

107.3377 

916.8433 

2 

123.0457 

1204.8226 

2 

138.7537 

1532.0718 

3 

107.5995 

921.3211 

3 

123.3075 

1209.9550 

3 

139.0155 

1537.8587 

4 

107.8613 

925.8099 

4 

123.5693 

1215.0982 

4 

139.2773 

1543.6565 

5 

108.1231 

930.3096 

5 

123.8311 

1220.2524 

5 

139.5391 

1549.4651 

6 

108.3849 

934.8202 

6 

124.0929 

1225.4175 

6 

139.8009 

1555.2847 

7 

108.6467 

939.3417 

7 

124.3547 

1230.5935 

7- 

140.0627 

1561.1152 

8 

108.9085 

943.8741 

8 

124.6165 

1235.7804 

8 

140.3245 

1566.9566 

9 

109.1703 

948.4174 

9 

124.8783 

1240.9782 

9 

140.5863 

1572.8089 

10 

109.4321 

952.9716 

10  125.1401 

1246.1869 

10 

140.8481 

1578.6721 

11 

109.6939 

957.5367 

11  j  125.4019 

1251.4065 

11  !  141.1099 

1584.5462 

TABLE  NO.  73— CON.  181 

From    I  raul  \\  in*    x  ••  civil   LH^HMMT  s  Pocket  Book." 


CIRCLES. 

TABLE   3   OF   C'lRCL-ES— (Continued). 
Plain*  in  units  and  twelfths;   as  in  feet  and  inches. 


Dia. 

Circumf. 

Area. 

Dia.  Circumf, 

Area. 

Dia. 

Circumf 

Area. 

Ft.In. 

Feet. 

Sq.  ft. 

Ft.In.   Feet. 

Sq.  ft. 

Ft.Ia. 

Feet. 

Sq.  ft. 

45  0 

141.3717 

1590.4313 

50  0  157.0796  1963.4954 

55  0 

172.7876  2375.8294 

1 

141.6335 

1596.3272 

1  157.3414  •  1970.0458 

1 

173.0494 

2383.0314 

2 

141.8953 

1602.2341 

2  157.6032  1976.6072 

2  173.3112  2390.2502 

3 

142.1571 

1608.1518 

3  157.8650  1983.1794 

3  173.5730  2397.4770 

4 

142.4189 

1614.0805 

4  158.1268  :  1989.7626 

4  173.8348  2404.7146 

5 

142.6807 

1620.0201 

5  158.3886  1996  3567 

5 

174.0966  2411.9632 

6 

142.9425 

1625.9705 

6  158.6504  ,  2002.9617 

6 

174.3584  2419.2227 

7 

143.2043 

1631.9319 

7  i  158.9122  2009.5776 

7 

174.6202  2426.4931 

8 

143.4661 

1637.9042 

8  159.1740  2016.2044 

8 

174.8820  2433.7744 

9 

143.7279 

1643.8874 

9  159.4358  2022.8421 

9 

175.1438 

2441.0666 

10 

143.9897 

1649.8816 

10  i  159.6976  !  2029.4907 

10 

175.4056 

2448.3697 

11 

144.2515 

1655.8866 

11 

159.9594  i  2036.1502 

11 

175.6674  !  2455.6837 

46  0 

144.5133 

1661.9025 

51  0 

160.2212  2042.8206 

56  0 

175.9292  !  2463.0086 

1 

144.7751 

1667.9294 

1  160.4830  :  2049.5020 

1 

176.1910  2470.3445 

2 

145.0369 

1673.9671 

2  160.7448  2056.1942 

2 

176.4528  2477.6912 

3 

145.2987 

1680.0158 

3  161.0060  2062.8974 

3 

176.7146  2485.0489 

4 

145.5605 

1686.0753 

4  161.2684  2069.6114 

4 

176.9764 

2492.4174 

5 

145.8223 

1692.1458 

5  161.5302  207*).  3364 

5 

177.2382  2499.7969 

6 

146.0841 

1698.2272 

6  i  161.7920  2083  0723 

6 

177.5000 

2507.1873 

7 

146.3459 

1704.3195 

7 

162.0538  2089.8191 

7 

177.7618 

2514.5886 

8 

146.6077 

1710.4227 

8 

162.3156 

2096.5768 

8 

178.0236  2522.0008 

9 

146.8695 

1716.5368 

9 

162.5774  I  2103.3454 

9 

178.2854  2529.4239 

10 

147.1313 

1722.6618 

10 

162.8392  2110.1249 

10 

178.5472  2536.8579 

11 

147.3931 

1728.7977 

11  163.1010 

2116.9153 

11 

178.8090  2544.3028 

47  0 

147.6549 

1734.9445 

52  0  163.3628 

2123.7166 

57  0 

179.0708  2551.7586 

1 

147.9167 

1741.1023 

1 

163.6246 

2130.5289 

1 

179.3326  2559.2254 

2 

148.1785 

1747.2709 

2 

163.8864 

2137.3520 

2 

179.5944 

2566.7030 

3 

148.4403 

1753.4505 

3  164.1482 

2144.1861 

3 

179.8562 

2574.1916 

4 

148.7021 

1759.6410 

4  164.4100 

2151.0310 

4 

180.1180 

2581.6910 

5 

148.9639 

1765.8423 

5  164.6718 

2157.8869 

5 

180.3798  2589.2014 

6 

149.2257 

1772.0546 

6  164.9336 

2164.7537 

6 

180.6416 

2596.7227 

7 

149.4875 

1778.2778 

7  165.1954 

2171.6314 

7 

180.9034 

2604.2549 

8 

149.7492 

1784.5119 

8  165.4572 

2178.5200 

8 

181.1652 

2611.7980 

,9 

150.0110 

1790.7569 

9  i  165.7190 

2185.4195 

9 

181.4270 

2619.3520 

10 

150.2728 

1797.0128 

10  165.9808 

2192.3299 

10 

181.6888  2626.9169 

11 

150.5346 

1803.2796 

11  166.2426 

2199.2512 

11 

181.9506  2634.4927 

48  0 

150.7964 

1809.5574 

>3  0  166.5044 

2206.1834 

58  0 

182.2124 

2642.0794 

1 

151.0582 

1815.8460 

1 

166.7662 

2213.1266 

1 

182.4742 

2649.6771 

2 

151.3200 

1822  1456 

2 

167.0280 

2220.0806 

2 

182.7360 

2657.2856 

3 

151.5818 

1828.4560 

3 

167.2898 

2227.0456 

3  182.9978  2664.9051 

4 

151.8436 

1834.7774 

4 

167.5516 

2234.0214 

4  183.2596  2672.5354 

5 

152.1054 

1841.1096 

5 

167.8134 

2241.0082 

5  183.5214  2680.1767 

6 

152.3672 

1847.4528 

6 

168.0752  2248.0059 

6  183.7832  :  2687.8289 

7 

152.6290 

1853.8069 

7 

168.3370  '  2255.0145 

7  184.0450  2695.4920 

8 

152.8908 

1860.1719 

8 

168.5988  2262.0340 

8  184.3068  2703.1659 

9 

153.1526 

1866.5478 

9 

168.8606  2269.0644 

9  184.5686  2710.8508 

10 

153.4144 

1872.9346 

10 

169.1224  2276.1057 

10  184.8:304  2718.5467 

11 

153.6762 

1879.3324 

11 

169.3842  2283.1579 

11  185.0922  2726.2534 

49  0 

153.9380 

188-3.7410 

54  0 

169.6460  2290.2210 

59  0  1  185.3540  ,  2733.9710 

1  | 

154.1998 

1892.1605 

1 

169.9078  2297.2951 

1  185.6158  2741.6995 

2 

154.4616 

1898.59,10 

2 

170.1696  2304.3800 

2 

185.8776  2749.4390 

3 

154.7234 

1905.0323 

3 

170.4314  2311.4759 

3 

186.1394 

2757.1893 

4 

154.9852 

1911.4846 

4 

170.6932  2318.5826 

4 

186.4012 

2764.9,506 

5 

155  2470 

1917.9478 

5 

170.9550  2325.7003 

5 

186.6630 

2772.7228 

6 

155.5088 

1924.4218 

6 

171.2168  2332.8289 

6 

186.9248 

2780.5058 

7 

155.7706  ! 

1930.9068 

7 

171.4786  2339.9684 

7 

187.1866 

2788.2998 

8 

156.0324 

1937.4027 

8 

171.7404  2347.1188 

8 

187.4484 

2796.1047 

9 

156.2942  i 

1943.9095 

9 

172.0022  \  2354.2801 

9 

187.7102 

2803.9205 

10 

156.5560  i 

1950.4273 

10 

172.2640  2361.4523 

10 

187.9720 

2811.7472 

11 

156.8178 

1956.9559 

11 

172.5258  j  2368.6354 

11 

188.2338 

2819.5849 

182  TABLE  NO.  73-CON. 

From  Traiitwine's  "Civil  Engineer's  PoeKet  Book. 


CIRCLES. 

TABLE   3  OF  CIRCLES— (Continued). 
Diams  in  units  and  twelfths;  as  in  feet  and  inches. 


Dia. 

Circumf. 

Area. 

Dia. 

Circumf. 

Area. 

Dia. 

Cireumf. 

Area. 

Ft.In. 

Feet. 

Sq.  ft. 

Ft.Iu. 

Feet. 

Sq.  ft. 

Ft.In. 

Feet. 

Sq.  ft. 

60  0 

188.4956 

2827.4334 

65  0 

204.2035 

3318.3072 

70  0 

219.9115 

3848.4510 

1 

188.7574 

2835.2928 

1 

204.4653 

3326.8212 

1 

220.1733 

3857.6194 

2 

189.0192 

2843.1632 

2 

204.7271 

3335.3460 

o 

220.4351 

3866.7988 

3 

189.2810 

2851.0444 

3 

204.9889 

3343.8818 

3 

220.6969 

3875.9890 

4 

189.5428 

2858.9366 

4 

205.1*507 

3352.4284 

4 

220.9587 

3885.1902 

5 

189.8046 

2866.8397 

5 

205.5125 

3360.9860 

5 

221.2205 

3894.4022 

6 

190.0664 

2874.7536 

6 

205.7743 

3369.5545 

6 

221.4823 

3903.6252 

7 

190.3282 

2882.6785 

7 

206.0361 

3378.1339 

7 

221.7441 

3912.8591 

8 

190.5900 

2890.6143 

8 

206.2979 

3386.7241 

8 

222.0059 

3922.1039 

9 

190.8518 

2898.5610 

9  206.5597 

3395.3253 

9 

222.2677 

3931.3596 

10 

191.1136 

2906.5186 

10 

206.8215 

3403.9375 

10 

222.5295 

3940.6262 

11 

191.3754 

2914.4871 

11  207.0833 

3412.5605 

11 

222.7913 

3949.9037 

61  0 

191.6372 

2922.4666 

66  0  207.3451 

3421.1944 

71  0 

223.0531 

3959.1921 

1 

191.8990 

2930.4569 

1  207.6069 

3429.8392 

1 

223.3149 

3968.4915 

2 

192.1608 

2938.4581 

2  207.8687 

3438.4950 

2 

223.5767  3977.8017 

3 

192.4226 

2946.4703 

3  208.1305 

3447.1616 

3 

223.8385  '  3987.1229 

4 

192.6843 

2954.4934 

4  208.3923 

3455.8392 

4 

224.1003 

3996.4549 

5 

192.9461 

2962.5273 

5  208.6541 

3464.5277 

5 

224.3621 

4005.7979 

6 

193.2079 

2970.5722 

6  208.9159 

3473.2270 

6 

224.6239 

4015.1518 

7 

193.4697 

2978.6280 

7  209.1777 

3481.9373 

7 

224.8857 

4024  5165 

8 

193.7315 

2986.6947 

8  !  209.4395 

3490.6585 

8 

225.1475 

4033.8922 

9 

193.9933 

2994.7723 

9  !  209.7013 

3499.3906 

9 

225.4093 

4043.2788 

10 

194.2551 

3002.8608 

10  209.9631 

3508.1336 

10 

225.6711 

4052.6763 

11 

194.5169 

3010.9602 

11  210.2249 

3516.8875 

11 

225.9329 

4062.0848 

62  0 

194.7787 

3019.0705 

67  0  210.4867 

3525.6524 

72  0 

226.1947 

4071.5041 

1 

195.0405 

3027.1918 

1 

210.74&5 

3534.4281 

1 

226.4565 

4080.9343 

2 

195.3023 

3035.3239 

2  211.0103 

3543.2147 

2 

226.7183 

4090.3755 

3 

195.5641 

3043.4670 

3  211.2721 

3552.0123 

3 

226.9801 

4099.8275 

4 

195.8259 

3051  .6209 

4 

211.5339 

3560.8207 

4 

227.2419 

4109.2905 

5 

196.0877 

3059.7858 

5 

211.7957 

&569.6401 

5 

227.5037 

4118.7643 

6 

196.3495 

3067.9616 

6 

212.0575 

3578.4704 

6 

227.7655 

4128.2491 

-  7 

196.6113 

3076.1483 

7 

212.3193 

3587.3116 

7 

228.0273 

4137.7448 

8 

196.8731 

3084.3459 

8 

212.5811 

3596.1637 

8 

228.2891 

4147.2514 

9  197.1349 

3092.5544 

9 

212.8429 

3605.0267 

9 

228.5509 

4156.7689 

10 

197.3967 

3100.7738 

10 

213.1047 

3613.9006 

10 

228.8127 

4166.2973 

11  !  197.6585 

3109.0041 

11 

213.3665 

3622.7854 

11 

229.0745 

4175.8366 

63  0 

197.9203 

3117.2453 

68  0 

213.6283 

3631.6811 

73  0 

229.3363 

4185.3868 

198.1821 

3125.4974 

1 

213.8901 

3640.5877 

1 

229.5981 

4194.9479 

2 

198.4439 

3133.7605 

2 

214.1519 

3649.5053 

2 

229  8599 

4204.5200 

3 

198.7057 

3142.0344 

3 

214.4137 

3658.4337 

3 

230.1217 

4214.1029 

4 

198.9675 

3150.3193 

4 

214.6755  36673731 

4 

230.3835 

4223.6968 

5 

199.2293 

3158.6151 

5 

214.9373  |  3676.3234 

5 

230.6453 

4233.3016 

6 

199.4911 

3166.9217 

6 

215.1991 

3685.2845 

6 

230.9071 

4242.9172 

7 

199.7529 

3175.2393 

7 

215.4609  3694.2566 

7 

231.1689 

4252.5438 

8 

200.0147 

3183.5678 

8  215.7227 

3703.2396 

8 

231.4307 

4262.1813 

9 

200.2765 

3191.9072 

9 

215.9845 

3712.2335 

9 

231.6925 

4271.8297 

10 

200.5383 

3200.2575 

10 

216.2463  i  3721.2383 

10 

231.9543 

4281.4890 

11 

200.8001 

3208.6188 

11  216.5081 

3730.2540 

11 

232.2161 

4291.1592 

64  0 

201.0619 

3216.9909 

69  0  216.7699 

3739.2807 

74  0 

232.4779 

4300.8403 

1 

201.3237 

3225.3739 

1  217.0317  3748.3182 

1 

232.7397- 

4310.5324 

2 

201.5855 

3233.7679 

2  217.2935  3757.3666 

2 

233.0015 

4320.2353 

3 

201.8473 

3242.1727 

3  217.5553  3766.4260 

3 

233.2633 

4329.9492 

4 

202.1091 

3250.5885 

4  217.8171  3775  4962 

4 

233.5251 

4339.6739 

5 

202.3709 

3259.0151 

5  218.0789 

3784.5774 

5 

233.7869 

4349.4096 

6 

202.6327 

3267.4527 

6  i  218.3407 

3793.6695 

6 

234.0487 

4359.1562 

7 

202.8945 

3275.9012 

7  218.6025 

3802.7725 

7 

234.3105 

4368.9136 

8 

203.1563 

3284.3606 

8  218.8643  3811.8864 

8 

234.5723 

4378.6820 

9 

203.4181 

3292.8309 

9 

219.1261  3821.0112 

9 

234.8341 

438,8.4613 

10 

203.6799 

3301.3121 

10  219.3879  3830.1469 

10 

235.0959 

4398.2515 

11 

203.9417 

3309.8042 

.  11  219.6497  3839.2935 

11 

285.8676 

4408.0526 

TABLE  NO.  73— CON.  183 

From  Traiit  wine's  "Civil  Engineer**  Pocket  Book." 

CIRCLE*. 

TABLE  3  OF   CIRCLES— (Continued). 
IManis  in  units  and  twelfths;   as  in  feet  ami  indies. 


Dia. 

Circumf.   Area. 

Dia.  {  Circumf. 

Area. 

Dia.  Circumf. 

A  rea. 

Ft.Iu. 

Feet. 

bq.  ft. 

Ft.In.   Feet. 

Sq.  ft. 

Ft.lu.   Feet. 

Sq.  ft. 

75  0 

235.6194 

4417.8647 

80  0 

251.3274 

5026.5482 

So  0 

267.0354 

5674..  ".«  -17 

1 

235.8812 

4427.6676 

1 

251.5892 

5037.0257 

1  267.2972 

5685.6K37 

2 

236.1430 

4437.5214 

2 

251.8510 

5047.5140 

2  !  267.5590 

5696.7765 

3 

236.4048 

4447.3662 

3 

252.1128 

5058.0133 

3  267.8208 

5707.9302 

4 

236.6666 

4457.2218 

4 

252.3746 

5068.5234 

4  268  0826 

5719.0919 

5 

236.9284 

4467.0884 

5 

252.6364 

5079.0445 

5 

268  3444 

5730.2705 

6 

237.1902 

4476.9659 

6 

252.8982 

5089.5764 

6 

268.6062 

5741.4509 

7 

237.4520 

4486.8543 

7 

253.1600 

5100.1193 

7 

268.8080 

5752.0543 

8 

237.7138 

4496.7536 

8 

253.4218 

5110.6731 

8 

269.1298 

5763.86-.-6 

9 

237.9756 

4506.6637 

9 

253.6836 

5121.2378 

9 

209.3916 

5775.08  IS 

10 

238.2374 

4516.5849 

10 

253.9454  « 

5131.8134 

10 

269.6534 

5780.3119 

11 

238.4992 

4526.5169 

11 

254.2072 

5142.3999 

11 

269.9152 

5797.5529 

76  0 

238.7610 

4536.4598 

81  0 

254.4690 

5152.9974 

86  0 

270.1770 

f,8U8  ftO-18 

1 

239.0228 

4546.4136 

1 

254.7308 

5163.6057 

1 

270.4388 

5820.0070 

2 

239.2846 

4556.3784 

2 

254.9926 

5174.2249 

2 

270.7006 

5831  3414 

3 

239.5464 

4566.3540 

3 

255.2544 

5184.8551 

3 

270.9024 

5842.6260 

4 

239.8082 

4576.3406 

4 

255.5162 

5195.4961 

4 

271  2242 

5853.9210 

5 

240.0700 

4586.3380 

5 

255.7780 

5206.1481 

5 

271.4860 

5805.2280 

6 

240.3318 

4596.3464 

6  256.0398 

5216.8110 

6 

271.7478 

5876.5454 

7 

240.5936  i  4606.3657 

7  256.3016 

5227.4847 

7 

272.0096 

5887.8737 

8 

240.8554 

4016.3959 

8  256.5634 

5238.1694 

8 

272.2714 

5899.21  2  '3 

9 

241.1172 

4626.4370 

9  256.8252 

5248.8650 

9 

272.5332 

5910..'  630 

10 

241.3790  4636.4890 

10  257.0870 

5259.5715 

10 

272.7950 

5921  l-24'> 

11 

241.6408  4646.5519 

11  257.3488 

5270.2889 

11 

273.0568 

5933  1959 

77  0 

241.9026  4656.6257 

82  0  1  257.6106 

5281.0173 

87  0 

2733180 

5944  i-7:>7 

1 

242.1644  4666.7104 

1  257.8724 

5291.7565 

1 

273.5804 

5956.0724 

2 

242.4262 

4676.8061 

2  258.1342 

5302.5066 

2  i  273.8422 

5967.4771 

3 

242.6880 

4686.9126 

3  258.3960 

5313.2677 

3 

274.1040 

5978.8926 

4 

242.9498  4697.0301 

4  258.6578 

5324.0396 

4 

274.3658 

5990.3191 

5 

243.2116  i  4707.1584 

5 

258.9196 

5334.8225 

5 

274.6270 

6001.7504 

6 

243.4734  4717.2977 

6 

259.1814 

5345.6162 

6 

274.8894 

6013.2047 

7 

243.7352 

4727.4479 

7 

259.4432 

5356.4209 

7 

275.1512 

6024.6039 

8 

243.9970 

4737.6090 

8 

259.7050 

5367.2365 

8 

275.4130 

6036.134* 

9 

244.2588 

4747.7810 

9 

259.9668 

5378.0630 

9 

275.6748 

6047.6149 

10 

244.5206 

4757.9639 

10 

260.2286 

5388.9004 

10  i  275.9366 

6059.106* 

11 

244.7824 

,4768.1577 

11 

260.4904 

5399.7487 

11  276.1984 

6070.6091 

78  0 

245.0442  4778.3624 

83  0 

260.7522 

5410.6079 

88  0  276.4602 

6082.1234 

1 

245.3060  4788.5781 

1 

261.0140 

5421.4781 

1  276.7220 

6093.6480 

2 

245.5678  4798.8046 

2 

261.2758 

5432.3591 

2  276.9838 

6105.1835 

3 

245.8296  ,  4809.0420 

3  261.5376 

5443.2511 

3  277.2456 

6116.7300 

4 

246.0914  4819.2904 

4  261.7994 

5454.1539 

4  277.5074 

6128.2873 

5 

246.3532  4829.5497 

5  262.0612 

5465.0677 

5  !  277.7692 

6139.8556 

6 

246.6150  4839.8198 

6  262.3230 

5475.9923 

6  278.0309 

6151.434& 

7  246.8768  4850.1009 

7  262.5848 

5486.9279 

7  278.2927 

6163.0.48 

8  247.1386  4860.3929 

8  i  262.8466 

5497.8744 

8  278.5545 

6174.6253 

9  247.4004  4870  6958 

9  263.1084 

5508-8318 

9  i  278.8163 

6186.2377 

10  •247.6622  4881.0096 

10  263.3702 

5519.8001 

10  i  279.0781 

6197.8605 

11  247.9240  4891.3343 

11  263.6320 

5530.7793 

11  i  279.3399 

6209.4942 

T9  9  248.1858  i  4901.6699 

84  0 

263.8938 

5541.7694 

89  0  i  279.6017 

6221.1389 

1  248.4476  4912.0165 

1  264.1556 

5552.7705 

1  279.863.') 

6232.7944 

2  248.7094  4922.3739 

2  264.4174 

5563.7824 

2 

280.1253 

6244.460* 

3  248.9712  i  4932.7423 

3 

264.6792 

5574.8053 

3 

280.3871 

6250.1:>si: 

4  249.2330  4943.1215 

4  264.9410 

5585.8390 

A 

280.6489 

6267.8264 

5  249.4948  4953.5117 

5  265.2028 

5596.8837 

5 

280.9107 

6279.  52-V, 

6  249.7566  4963.9127 

6  !  265.4646 

5607.9392 

6 

281.1725 

6291.235»> 

7  250.0184  4974.3247 

7  265.7264 

5619.0057 

7 

281.4343 

0:;i)2  95M 

8  250.2802  4984.7476 

8  265.9882 

5630.0831 

8 

281.6961 

6314.6885 

9  250.5420  4995.1814 

9  26*3.2500 

5641.1714 

9 

281.9579 

6326.4313 

10  250.8038  5005.6261 

10  266.5118 

5652.2706 

10 

282.2197 

6338.1850 

11  251.0656  5016.0817 

11  266.7736 

5663.3807 

11 

282.4815 

6349.9496 

H  TABLE  NO.  73— COJSTCL. 

From  Traiitwine's  "Civil  Fii$;-iiiccr*N  Pocket  Book.' 


CIRCLES. 

TABLE   3  OF   CIRCLES— (Continued). 
in  units  and  twelfths;  as  in  feet  and  inches. 


Dia.  Circumf. 

! 

Area. 

Dia. 

Circumf.   Area. 

Dia. 

Circuraf. 

Area. 

Ft.In.  !  Feet. 

Sq.  ft. 

Ft.In. 

Feet. 

Sq.  ft. 

Ft.In. 

Feet. 

Sq.  ft. 

90  0  282.7433 

6361.7251 

1)3  5 

293.4771 

6853.9134 

96  9 

303.9491 

7351.  7C86 

1  283.0051 

6373.5116 

6 

293.7389 

6866.1471 

10 

304.2109 

7364.4386 

2  283.2669 

6385.3089 

7 

294.0007  !  6878.3917 

11 

304.47L7 

7377.1195 

3  !  283.5287 

6397.1171 

8 

294.2625  6890.6472 

97  0 

304.7345 

73C9.8113 

4  !  283.7905 

6108.1)303 

9 

294.5243  6902.9135 

1 

304.9963 

7402.5140 

5  !  284.0523 

6420.7663 

10 

294.7861  '  6915.1908 

2 

305.2581 

7415.2277 

6  i  284.3141 

6432.6073 

11 

295.0479  6927.4791 

3 

305.5199 

7427.9522 

7  284.5759 

6444.4592 

94  0 

295.3097  I  6939.7782 

4 

305.7817 

7440.6877 

8  :  284.8377 

6156.3220 

1 

295.5715  !  6952.0882 

5 

306.0435 

7453.4340 

9  i  28').  0995 

6168.1957 

2 

295.8333  <  6964.4091 

6 

306.3053 

7466.1913 

10  |  285.3613 

6180.0803 

3 

296.0951 

6976.7410 

7 

306.5671 

7478.C595 

11  '  285.0231 

6491.97o8 

4  I  29*3569  6989.0837 

8 

306.8289 

7491.7385 

11  0  2858849 

6503.882-J 

5 

296.6187 

7001.4374 

9 

307.0907 

7504.5285 

1  286.1467 

6515.7995 

6 

296.8805 

7013.8019 

10 

307.3525 

7517.32SJ 

2  286-408-') 

6527.7278 

7 

297.1423 

7026.1774 

11 

307.6143 

7530.141i 

3  286.6703 

6539.6669 

8 

297.4041 

7038.5638 

98  0 

307.8761 

7542.S640 

4  286.9321 

6551.6169 

9 

297.6059 

7050.9611 

1 

308.1379 

75C5.7976 

5  287.1939 

6563.5779 

10 

297.9277 

7063.3693 

2 

308.3997 

7568.0.421 

6  1  287.4557 

6575.5498 

11 

298.1895 

7075.7884 

3 

308.6615 

7581.4176 

7  287.7175 

6587.5325 

95  0 

298.4513 

7088.2184 

4 

308.92£3 

7594.SG39 

8  '  287.9793 

6599.5262 

1 

298.7131 

7100.6593 

5 

309.1851 

7607.2H2 

9  2882411 

0611.5308 

2  I  298.9749 

7113.1112 

6 

309.4469 

7620.1293 

10  288.5029 

6623.5463 

3  |  299.2367 

7125.5739 

7 

309.7087 

7633.0284 

11  2887647 

6635.5727 

4  299.4985 

7138.0476 

8 

309.9705 

764f.e884 

92  0  i  289.0265 

6647.6101 

5 

299.7003 

7150.5321 

9 

310.2323 

7658.8593 

1  1  289.2883 

(Kv'9.6583 

6 

300.0221 

7163.0276 

10 

310.4941 

7671.7911 

2  289.5501 

0671.7174 

7  300.2839 

7175.5340 

11 

310.7559 

7684.7338 

3  289.8119 

6683.7875 

8  300.5457 

7188.0513 

99  0 

311.0177 

7697.6874 

4  290.0737 

6695.8684 

9  300.8075 

7200.5794 

1 

311.2795 

7710.6519 

5  290.3355 

6707.9603 

10  301.0693 

7213.1185 

2 

311.5413 

7723.6274 

6  290.5973 

6720.0630 

11  301.3311 

7225.6686 

3 

311.8031 

7736.6137 

7  290.8591 

0732.1767 

96  0  301.5929  7238.2295 

4 

312.0649 

7749.6109 

8  291.1209 

0744.3013 

1  301.8547  7250.8013 

5 

312.3267 

7762.6191 

9  291.3827 

6756  4368 

2  302.1165  7263.3840 

6 

312.5885 

7775.6382 

10  291.6145 

67(58.5832 

3  302.3783  7275.9777 

7 

312.8503 

7788.6681 

11  291.9063 

6780.7405 

4  302.6401  7288.5822 

8 

313.1121 

7801.7090 

93  0  292.1681 

6792.9087 

5  302.9019  7301.1977 

9 

313.3739 

7814.7608 

1  292.4299 

6805.0878 

6  303.1637  7313.8240 

10 

313.6357 

7827.8235 

2  292.6917 

68172779 

7  303.4255  7326.4613 

11 

313.8975 

7840.8i'71 

3  292.9535 

6829.4788 

8  303.6873 

7339.1095 

100  0 

314  J  593 

7853.9816 

4  293.2153 

6841.6907 

Circumferences  in  feet,  when  the  diam  contains  fractions 
of  ail  inch.     See  similar  process,  p  177 


Diam.      Circumf. 

Diam,       Circuraf, 

Diam, 

Circumf, 

Diam, 

Circumf, 

Diam, 

Circumf, 

Inch.       foot 

inch         foot 

Inch 

foot. 

inch. 

foot. 

inch. 

foot. 

1-64 

.004091 

7-32      .057269 

27-64 

.110447 

5-8 

.163625 

53-64 

.216803 

1-32 

.008181 

15-64 

.061359 

7-16 

.114537 

41-64 

.167715 

27-32 

.220S93 

3-64 

.012272 

& 

.065450 

29-64 

.1186-28 

21-32 

.171806 

55-64 

.2249S4 

1-16 

.016362 

17-64 

.069540 

15-32 

.122718 

43-64 

.175896 

7-8 

.229074 

5-64 

.020453 

9-32 

.0736M1 

31-64 

.126809 

11-16 

.179987 

57-64 

.233165 

3-32 

.024544 

19-64 

.077722 

% 

.130900 

45-64 

.184078 

29-32 

.237256 

7-64 

.028634 

5-16 

.081812 

aOi 

.134990 

23-32 

.188168 

59-64 

.241346 

X 

.0327-25 

21-64 

.085903 

17-32 

.139081 

47-64 

.192259 

15-16 

.245437 

9-64 

.036S16 

11-32 

.089994 

35-64 

.143172 

% 

.196350 

61-64 

.249528 

5-32 

.04090(5 

23-64 

.094084 

9-16 

.147262 

49-64 

.200440 

31-32  1  .253618 

11-64 

.044997 

% 

.098175 

37-64  |   .151353 

25-32 

.204531 

63-64  |  .257709 

3-16 

.049087 

25-04 

.102265 

19-32      .155443 

51-64 

.208621 

1 

.261799 

13-64  1  .<  153178 

13-32 

.106356 

39-64       .159534 

13-16 

.212712 

TABLE  NO.  74.  185 

From  Trautwine's  "Civil  Engineer's  Pocket  Rook." 

SQUARE  AND  CUBE   ROOTS. 
Square  Roots  and  Cube  Roots  of  X timbers  from  .1  to  28. 

No  errors. 


No. 

Square. 

Cube. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

No. 

Sq.  Rt. 

C.  Rt. 

.1 

.01 

.001            .316 

.464 

.7 

2.387 

1.786 

_4 

3.661 

2.375 

.15 

.0225 

.0034          .387 

.531 

.8 

2.408 

1.797 

.6 

3.68K 

2.387 

.2 

.04 

.008            .447 

.585 

.9 

2.429 

1.807 

.8 

3.715 

2.399 

.25 

.0625 

.0156          .500 

.630 

6. 

2.449 

1.817 

14. 

3.742 

2.410 

.3 

.09 

.027    '        .548 

.669 

.1 

2.470 

1.827 

.2 

3.768 

2.422 

.35 

.1225 

.0429  .'        .592 

.705 

,| 

2.490 

1.837 

.4 

3.795 

2.433 

.4 

.16 

.064            .633 

.737 

.3 

2.510 

1.847 

.6 

3.821 

2.444 

.45 

.2025 

.0911  I        .671 

.766 

.4 

2.530 

1.857 

.8 

3.847 

2.455 

.5 

.25 

.125            .707 

.794 

.5 

2.550 

1.866 

15. 

3.873 

2.466 

.55 

.3025 

.1664  1        .742 

.819 

.6 

2.569 

1.876 

.2 

3.899 

2.477 

.6 

.36 

.216            .775 

.843 

.7 

2.588 

1.885 

.4 

3.924 

2.488 

.65 

.4225 

.2746          .806 

.866 

.8 

2.608 

1.895 

.6 

3.950 

2.499 

.7 

.49 

.343 

837 

.888 

.9 

2.627 

1.904 

.8 

3.975 

2.509 

.75 

.5625 

.4219 

.866 

.909 

7. 

2.646 

1.913 

16. 

4. 

2.520 

.8 

.64 

.512            .894 

.928 

.1 

2.665 

1.922 

.2 

4.025 

2.530 

.85 

.7225 

.6141  1        .922 

.947 

.2 

2.683 

1  .931 

.4 

4.050 

2.541 

,9 

.81 

.729            .949 

.965 

.3 

2.702 

1.940 

.6 

4.074 

2.551 

.95 

.9025 

.8574          .975 

.983 

.4 

2.720 

1.949 

.8 

4.099 

2.561 

1. 

1.000 

1.000          1.000 

1.000 

.5 

2.739 

1.957 

17. 

4.123 

2.571 

.05 

1.103 

1.158 

1.025 

1.016 

.6 

2.757 

1.966 

.2 

4.147 

2.581 

1.1 

1.210 

1.331 

1.049 

1.032 

.7 

2.775 

1  975 

.4 

4.171 

2.591 

.15 

1.323 

1.521 

1.072 

1.018 

.8 

2.793 

1.983 

.6 

4.195 

2.601 

1.2 

1.440 

1.728 

1.095 

1.063 

.9 

2.811           1.91)2 

.8 

4.219 

2.611 

.25 

1.563 

1.963 

1.118 

1.077 

8. 

2.828     i     2.000 

18. 

4.243 

2.621 

1.3 

1.690 

2.197 

1.140 

1.091 

.1 

2.846          2.008 

.2 

4.266 

2.630 

.35 

1.823 

2.460 

1.162 

1.105 

.2 

2.864          2.017 

.4 

4.290 

2640 

1.4 

1.960 

2.744 

1.183 

1.119 

J 

2.881          2.025 

•6 

4.313 

2.650 

.45 

2.103 

3.049 

1.204 

1.132 

.4 

2.898          2.033 

.   -8 

4.336 

2.659 

1.5 

2.250 

3.375 

1.225 

1.145 

2.915          2.041 

19. 

4.359 

2.668 

.55 

2.403 

3.724 

1.245 

1.157 

Jt 

2.933          2.0  19 

.2 

4.382 

2.678 

1.6 

2.560 

4.096 

1.265 

1.170 

.7 

2.950     ;     2.057 

.4 

4.405 

2.687 

.65 

2.723 

4.492 

1.285 

1.182 

.8 

2.966     j     2.065 

.6 

4.427 

2.696 

1.7 

2.890 

4.913 

1.304 

1.193 

.9 

2.983          2.072 

.8 

4.450 

2.705 

.75 

3.063 

5.359 

1.323 

1.205 

9. 

3.                2.080 

20. 

4.472 

2.714 

1.8 

3.240 

5.832 

1.342 

1.216 

.1 

3.017          2.088 

.2 

4.494 

2.723 

.85 

3.423 

6.332 

1.360 

1.228 

.2 

3.033          2.095 

.4 

4.517 

2.732 

1.9 

3.610 

6.859 

1.378 

1.239 

.3 

3.050     1     2.103 

.6 

4.539 

2.741 

.95 

3.803 

7.415 

1.396 

1.249 

.4 

3.066     !     2.110 

.8 

4.561 

2.750 

«.       !       4.000 

8.000 

1.414 

1.260 

.5 

3.082          2.118 

21. 

4.583 

2.759 

.1            4.410 

9.261 

1.449 

1.281 

.6 

3.098          2.125 

.2 

4.604 

2.768 

.2           4.840 

10.65 

1.483 

1.301 

.7 

3.114     I     2.133 

.4 

4.626 

2.776 

.3           5.290 

12.17 

1.517 

1.320 

.8 

3.130     ;     2.140 

.6 

4.648 

2.785 

.4 

5.760 

13.82 

1.549 

1.339 

.9 

3.146          2.147 

.8 

4.669 

2J94 

-5 

6.250 

15.63 

1.581 

1.357 

10.     ' 

3.162     :     2.154 

22. 

4.690 

2.802 

.6 

6.760 

-47.58 

1.612 

1.375 

.1 

3.178          2.162 

.2 

4.712 

2.810 

.7 

7.290 

19.68 

1.643 

1.392 

.2 

3.194          2.169 

.4 

4.733 

2.819 

.8 

7.840 

21.95 

1.673 

1.409 

.3 

3.209     j     2.176 

.6 

4.754 

2.827 

.9 

8.410 

24.39 

1.703 

1.426 

.4 

3.225           2.183 

.8 

4.775 

2.836 

8. 

9. 

27. 

1.732 

1.442 

.5 

3.240 

2.190 

23. 

4.7»6 

2.844 

.1     :       %.61 

29.79 

1.761 

1.458 

.6 

3.256          2.197 

.2 

4.817 

2.852 

.2     !     10.24 

32.77 

1.789 

1.474 

.7 

3.271           2.204 

.4 

4.837 

2.860 

.»     j     10.89 

35.94 

1.817 

1.489 

.8 

3.286          2.210 

.6 

4.858 

2.868 

.4          11.56 

39.30 

I.b44 

1.504 

.9 

3.302          2.217 

.8 

4.879 

2.876 

.5          12.25 

42.88 

1.871 

1.518 

11. 

3.317           2.224 

24. 

4.899 

2.884 

.6 

12.96 

46.66 

1.897 

1.533 

.1 

3.332          2.2*1 

.2 

4.919 

2.892 

13.69 

50.65 

1  .924 

1.547 

.2 

3.347          2.  287 

.4 

4.940 

2.900 

is          14.44 

54.87 

1.949 

1.560 

.3 

3.362          2.244 

.6 

4.960 

2.908 

.9         15.21 

59.32 

1.975 

1.574 

.4 

3  376          2.251 

.8 

4.980 

2.916 

4.           16. 

64. 

2. 

1.587 

.5 

3.391           2.257 

25. 

5. 

2.924 

.1 

16.81 

68.92 

2.025 

1.601 

.« 

3.406          2.264 

.2 

5020 

2.932 

.2 

17.64 

74.09 

2.049 

1  613 

.7 

3.421           2.270 

.4 

5.040 

2.940 

.3          18.49 

79.51            2.074 

1.626 

.8 

3.435          2.277 

.6 

5.060 

2.947 

.4 

19.36 

85.18           2.098 

1  .6:59 

.9 

3.450     j     2.283 

.8 

5.079 

2.955 

.5          20.25 

91.13 

2.121 

1.651 

12. 

3.464           2  2H9 

26. 

5099 

2.962 

.6          21.16 

97.34 

2.145 

1.663 

.1 

3479          2.296 

.2 

5.119 

2.970 

.7     :     22.09 

103.8 

2.168 

1.675 

.2 

3.493          2.302 

4 

5.138 

2.978 

.8          23.04 

110.6             2.191 

1.687 

.3 

3.507          2.308 

.6 

5.158 

2.985 

.9          24.01 

117.6              2.214 

1.69*- 

.4 

3.521           2.315 

.8 

5.177 

2.993 

6.           25. 

125.                 2.  286 

1.710 

5 

3.536          2.321 

27. 

5.196 

3.000 

1          26.01 

182.  7 

2.258 

1.721 

!6 

3.550          2.327 

.2 

5.215 

3.007 

.2          27.04 

140.6              2.280 

1.732 

.7 

3.564          2.333 

.4 

5.235 

3.015 

.3     ,     28.09 

14K9              2.302 

1.744 

.8    j     3.578          2  339 

.6 

5.254 

3.022 

.4          29.16 

!     157.5 

2.324 

1.754 

.9         3.592          2.345 

.8 

5.273 

3.029 

.5     i     3C.25 

166.4 

2.345 

,        1.7«T 

13. 

3.306          2.351 

28. 

5.292 

3.037 

.6         31.36 

175.6              2.36<J 

i     1.77« 

.2 

3  «H3      ;      2.363 

.2           5.310 

3.044 

To  find  roots  by  logarithms    see  Pages  200  and  202. 


186  TABLE  NO.  To. 

From  Trautwine's  «•  Civil  Engineer's  Pocket  Book/9 

SQUARES,  CUBES,  AND  ROOTS. 


TABLE  of  Squares,  Cubes.  Square  Roots,  and  Cube  Roots, 
of  Numbers  from  1  to  1OOO. 

REMARK  ON  THE  FOLLOWING  TABLK.     Wherever  the  effect  of  a  fifth  decimal  in  the  roots  would  be  t» 
fcdd  1  to  the  fourth  and  final  decimal  in  the  table,  the  addition  has  been  made.  No  errors. 


No. 

Square. 

Cube. 

Sq.  Rt. 

C.  Rt. 

No. 

Square 

Cube. 

Sq.  Rt. 

C.Rt. 

1 

1 

l 

1.0000 

1.0000 

61 

3721 

226981 

7.8102 

3.9365 

2 

4 

8 

1.4142 

1.2599 

62 

3844 

238328 

7.8740 

3.9579 

3 

9 

27 

1.7321 

1.4422 

63 

3969 

250047 

7.9373 

3.9791 

4 

16 

64 

2.0000 

1.5874 

64 

4096 

262144 

8.0000 

4. 

5 

25 

125 

2.2361 

1.7100 

65 

4225 

274625 

8.0623 

4.020T 

6 

36 

216 

2.4495 

1.8171 

66 

4356 

287496 

8.1240 

4.0412 

7 

49 

343 

2.6458 

1.9129 

67 

4489 

300763 

8.1854 

4.0615 

8 

64 

512 

2.8284 

2.0000 

68 

4624 

314432 

8.2462 

4.0817 

9 

81 

729 

3.0000 

2.0801 

69 

4761 

328509 

8.3066 

4.1016 

10 

100 

1000 

3.1623 

2.1544 

70 

4900 

343000 

8.3666 

4.1213 

11 

121 

1331 

3.3166 

2.2240 

71 

5041 

357911 

8.4261 

4.1408 

12 

144 

1728 

3.4641 

2.2894 

72 

5184 

373248 

8.4853 

4.1602 

13 

169 

2197 

3.6056 

2.3513 

73 

5329 

389017 

8.5440 

4.1795 

14 

196 

2744 

3.7417 

2.4101 

74 

5476 

405224 

8.6023 

4.1983 

15 

225 

3375 

3.8730 

2.4662 

75 

5625 

421875 

8.6603 

4.2172 

16 

256 

4096 

4.0000 

2.5198 

76 

5776 

438976 

8.7178 

4.2358 

17 

289 

4913 

4.1231 

2.5713 

77 

5929 

456533 

8.7750 

4.2543 

18 

324 

5832 

4.2426 

2.6207 

78 

6084 

474552 

8.8318 

4.2727 

19 

361 

6859 

4.3589 

2.6684 

79 

6241 

493039 

8.8882 

4.2908 

20 

400 

8000 

4.4721 

2.7144 

80 

6400 

512000 

8.9443 

4.3089 

21 

441 

9261 

4.5826 

2.7589 

81 

6561 

531441 

9. 

4.3267 

22 

484 

10648 

4.6904 

2.8020 

82 

6724 

551368 

9.0554 

4.3445 

23 

529 

12167 

4.7958 

2.8439 

83 

6889 

571V87 

9.1104 

4.3621 

24 

576 

13824 

4.8990 

2.8845 

84 

7056 

592704 

9.1652 

4.3795 

25 

625 

15625 

5.0000 

2.9240 

85 

7225 

614125 

9.2195 

4.3968 

26 

676 

17576 

5.0990 

2.9625 

86 

7396 

636056 

9.2736 

4.4140 

27 

729 

19683 

5.1962 

3.0000 

87 

7569 

658503 

9.3274 

4.4310 

28 

784 

21952 

5.2915 

3.0366 

88 

7744 

681472 

9.3808 

4.4480 

29 

841 

24389 

5.3852 

3.0723 

89 

7921 

704969 

9.4340 

4.4647 

30 

900 

27000 

5.4772 

3.1072 

90 

8100 

729000 

9.4868 

4.4814 

31 

961 

29791 

5.5678 

3.1414 

91 

8281 

753571 

9.5394 

4.4979 

32 

1024 

32768 

5.6569 

3.1748 

92 

8464 

778688 

9.5917 

4.5144 

33 

1089 

35937 

5.7446 

3.2075 

93 

8649 

804357 

9.6437 

4.5307 

34 

1156 

39304 

5.8310 

3.2396 

94 

8836 

830584 

9.6954 

4.5468 

35 

1225 

42875 

5.9161 

3.2711 

95 

9025 

857375 

9.7468 

4.5629 

36 

1296 

46656 

6.0000 

3.3019 

96 

9216 

884736 

9.7980 

4.5789 

37 

1369 

50653 

6.0828 

3.3322 

97 

9409 

912673 

9.8489 

4.5947 

38 

1444 

54872 

6.1644 

3.3620 

98 

9604 

941192 

9.8995 

4.6104 

39 

1521 

59319 

6.2450 

3.3312 

99 

9891 

970299 

9.9499 

4.6261 

40 

1600 

64000 

6.3246 

3.4200 

100 

10000 

1000000 

10. 

4.6416 

41 

1681 

68921 

6.4031 

3.4482 

101 

10201 

1030301 

10.0499 

4.6570 

42 

1764 

74088 

6.4807 

3.4760 

102 

10404 

1061208 

10.0995 

4.6723 

43 

1849 

79507 

6.5574 

3.5034 

103 

10609 

1092727 

10.1489 

4.6875 

44 

1936 

85184 

6.6332 

3.5303 

104 

10816 

1124864 

10.1980 

4.7027 

45 

2025 

91125 

6.7082 

3.5569 

105 

11025 

1157625 

10.2470 

4.7177 

46 

2116 

97336 

6.7823 

3.5830 

106 

11236 

1191016 

10.2956 

4.7328 

47 

2209 

103823 

6.8557 

3.6088 

107 

11449 

1225043 

10.3441 

4.7475 

48 

2304 

1  10592 

6.9282 

3.6342 

108 

11664 

1259712 

10.3923 

4.7622 

49 

2401 

117649 

7.0000 

3.6593 

109 

11881 

1295029 

10.4403 

4.7769 

50 

2500 

125000 

7.0711 

3.6840 

110 

12100 

1331000 

10.4881 

4.7914 

51 

2601 

132651 

7.1414 

3.7084 

111 

12321 

1367631  |  10.5357 

4.8059 

52 

2704 

140608 

7.2111 

3.7325 

112 

12544 

1404928    10.5830 

4.8203 

53 

2809 

148877 

7.2801 

3.7563 

113 

12769 

1442897  I  10.6301 

4.a346 

54 

2916 

157464 

7.3485 

3.7798 

114 

12996 

1481544 

10.6771 

4.8488 

55 

3025 

166375 

7.4162 

3.8030 

115 

13225 

1520875 

10.7238 

4.8629 

56  !   3136 

175616 

7.4833 

3.8259 

116 

13456 

15608% 

10.7703 

4.8770 

57  !   3249 

185193 

7.5498 

3.8485 

117 

13689 

1601613 

10.8167 

4.8910 

68     3364 

195112 

7.6158  !   3.8709 

118 

13924 

1643032 

10.8628 

4.9049 

59     3481 

205379 

7.6X11     3.8930 

119    14161 

1685159 

10.9087 

4.9187 

60  '   3600 

216000 

7.7460     3.9149 

120    14400    1728000 

10.9545 

4.93* 

TABLE  NO.  75-CON.  187 

From  Trautwine's  "  Civil  Engineer's  Pocket  Book." 


SQUARES,  CUBES,  AND   ROOTS. 

TABLE  of  Squaros,  mix's.  Sqmtre  Roots.  an<l  Cube  Roots, 
of  Numbers  from  1  to  1OOO  — (CONTINUED  ) 


No. 

Square. 

Cube. 

Sq.  Rt. 

C.  Rt. 

No. 

Square. 

Cube. 

Sq.  Rt 

C.  Rt. 

121 

14641 

1771561 

11. 

4.9461 

86 

34596 

6434856 

8.4MH 

5.7083 

122 

14884 

1815848 

11.0454 

4.9597 

87 

34969 

6539203 

3.6748 

5.7185 

123 

15129 

1860867 

11.0905 

4.9732 

88 

35344 

6644672 

3.7113 

5.7287 

124 

15376 

1906624 

11.1,  '555 

4.9866 

89 

35721 

6751269 

3.7477 

5.7388 

125 

15625 

1953125 

11.1803 

5. 

90 

36100 

6859000 

3.7840 

5.7489 

126 

15876 

2000376 

11.2250 

5.0133 

91 

36481 

6967871 

13.8203 

5.7590 

127 

16129 

204oo83 

11.2694 

5.0265 

92 

36864 

7077888 

13.8564 

5.7690 

128 

16381 

2097152 

11.3137 

5.0397 

93 

37249 

7189057 

13.85)21 

5.7790 

129 

16641 

2146689 

11.3578 

5.0528 

94 

37636 

7301381 

13.9284 

5.7890 

130 

16900 

2197000 

11.4018 

5.0658 

95 

38025 

7414875 

13.9642 

5.7989 

131 

17161 

2248091 

11.4455 

5.0788 

196 

38416 

7529536 

14. 

5.8088 

132 

17424 

22995)68 

11.4891 

5.0916 

197 

38809 

7645373 

14.0357 

5.8186 

134 

17958 

2406104 

11.  '5758 

5^1172 

199 

39601 

788059?) 

14.1067 

5.8383 

136 

18225 

2460375 

11.6190 

5.1299 

200 

40000 

8000000 

14.1421 

5.8480 

136 

18496 

2515456 

11.6619 

5.1426 

201 

40401 

8120601 

14.1774 

5.8578 

137 

18769 

2571353 

11.7047 

5.1551 

202 

40804 

8242408 

14.2127 

5.8675 

138 

19044 

2628072 

11.7473 

5.1676 

203 

41209 

8365427 

14.2478 

5.8771 

139 

19321 

2685619 

11.7898 

5.1801 

204 

41616 

8489664 

14.2829 

5.8868 

140 

19600 

2744000 

11.8322 

5.1925 

205 

420*25 

8615125 

14.3178 

5.8964 

141 

19881 

2803221 

11.8743 

5.2048 

206 

42436 

8741816 

14.3527 

5.9059 

142 

20164 

2863288 

11.9161 

5.2171 

207 

42849 

8869743 

14^3875 

5.9155 

143 

20449 

2924207 

11.9583 

5.2293 

208 

43264 

8998912 

14.4222 

5.9250 

144 

20736 

2985984 

12 

5.2415 

209 

43681 

9129329 

14.4568 

5.9345 

145 

21025 

3048625 

12.0416 

5.2536 

210 

44100 

9261000 

14.4914 

5.9439 

146 

21316 

3112136 

12.0830 

5.2656 

211 

44521 

9393931 

14.5258 

5.9538 

147 

21609 

3176523 

12,1244 

5.2776 

212 

44944 

9528128 

14.5602 

5.%27 

148 

21901 

3241792 

12.1G55 

5.2896 

213 

45369 

9663597 

14.5945 

5.9721 

149 

22201 

3307949 

12.2066 

5.3015 

214 

457% 

9800344 

14.6287 

5.9814 

150 

22500 

3375000 

12.2474 

5.3133 

215 

46225 

9938375 

14.6629 

5.9907 

151 

22801 

3442951 

2.2882 

53251 

216 

46656 

100776% 

14.6%9 

6. 

152 

23104 

3511808 

2.3288 

5.3368 

217 

47089 

10218313 

14.7309 

6.0092 

153 

23409 

3581577 

2.3693 

5.3485 

218 

47524 

10360232 

14.7648 

6.0185 

154 

23716 

3652254 

2.4037 

5.3601 

219 

47%1 

10503459 

14.7986 

6.0277 

155 

24025 

-  3723875 

2.4499 

5.3717 

220 

48400 

10648000 

14.8324 

6.0368 

156 

24336 

3796416 

12.4900 

5.3832 

221 

48841 

0793861 

14.8661 

6.0459 

157 

24649 

386^893 

12.5300 

5.3947 

222 

49284 

0941048 

14.8997 

6.0550 

158 

24964 

3941312 

12.5698 

5.4061 

223 

49729 

1089567 

14.9332 

6.0641 

159 

25281 

4019679 

12.6095 

5.4175 

224 

50176 

1239424 

14.9666 

6.0732 

160 

25600 

4096000 

12.6491 

5.4288 

225 

50625 

1390625 

,5. 

6.0822 

161 

25921 

4173281 

12.6886 

5.4401 

226 

51076 

1543176 

15.0333 

6.0912 

162 

26244 

4251528 

12.7279 

5.4514 

227 

51529 

1697083 

15.0665 

8.1002 

163 

26569 

4330747 

12.7671 

5.4626 

228 

51984 

1852352 

15.0997 

6.1091 

164 

26896 

4410344 

12.8062 

5.4737 

229 

52441 

2008989 

15.1327 

6.1180 

165 

27225 

4492125 

12.8452 

5.4848 

230 

52900 

2167000 

15.1658 

6.1269 

166 

27556 

45742% 

12.8841 

5.4959 

231 

53361 

2326391 

15.1987 

6.1358 

167 

27889 

4657463 

12.9228 

5.5069 

232 

53824 

2487168 

15.2315 

6.1446 

168 

28224 

4741632 

12.9615 

5.5178 

233 

54289 

2649337 

15.2643 

6.1534 

169 

28561 

4826809 

13. 

5.5288 

234 

54756 

2812904 

15.2971 

6.1622 

170 

28900 

4913000 

13.0384 

5.5397 

235 

55225 

2977875 

15.3297 

6.1710 

171 

29241 

5000211 

13.0767 

5.5505 

236 

55696 

31  14256 

15.3623 

6.1797 

If2 

29584 

5088448 

13.1149 

5.5613 

237 

56163 

H.U2053 

15.3948 

6.1885 

173 

29929 

5177717 

13.1529 

5.5721 

238 

56614 

3181272 

15.4272 

6.1972 

174 

30276 

5268024 

13.1909 

5.5828 

239 

57121 

3631919 

15.45% 

6.2058 

175 

30625 

5359375 

13.2288 

5.5934 

240 

5760C 

3821000 

15.4919 

6.2145 

176 

30976 

5451776 

13.2665 

5.6041 

241 

58081 

3997521 

5.5242 

6.2231 

177 

31329 

5545233 

13.3041 

5.6147 

242 

58564 

41721*8 

5.5563 

6.2317 

178 

316H4 

5639752 

13.3417 

5.6252 

243 

59019 

4348907 

5.5885 

6.2403 

179 

32041 

57H5.'{39 

13.3791 

5.6357 

244 

59536 

15267H1 

5.6205 

6.2488 

180 

32400 

5832000 

13.4164 

5.6462 

245 

60025 

4706125 

5.65  U5 

6.2573 

181 

32761 

5929741 

13.4536 

5.6567 

246 

60516 

4886936 

5.6844 

6.2658 

182 

33124 

6028568 

13.4907 

5.6671 

247 

61009 

5069223 

5.7162 

<>.2743 

183 

33489 

6128487 

13.5277 

5.6774 

248 

61504 

5252992 

15.7480 

6.2828 

184 

33856 

6229504 

13.5647 

5.6877 

249 

62001 

5438249 

]  5.  7797 

3.2912 

185 

34225 

6331625 

13.6015 

5.6980 

250 

62500 

15625000 

15.8114 

6.29M 

188  TABLE  NO.  75-CON. 

From  Traut wine**  ••  Civil  Engineer's  Pocket  Book.*9 

SQUARES,  CUBES,  AND  ROOTS. 

TABLE  of  Squares,  Cubes,  Square  Roots,  and  Cube  Roots, 
of  lumbers  from  1  to  1OOO  —  (CONTINUED.) 


No. 

Square. 

Cube. 

Sq.  Rt, 

C.  Rt. 

No. 

Square. 

Cube. 

Sq.  Rt. 

C.  Rt. 

511 
512 

261121 
262144 

133432831 
134217728 

22.6053 
22.6274 

7.9948 
8. 

576 
577 

331776 
332929 

191102976 
192100033 

24. 

24.0208 

8.3203 
8.3251 

513 

263169 

135003697 

22.6495 

8.0052 

578 

334084 

193100552 

24.0416 

8.3300 

514 

264196 

135796744 

22.6716 

8.0104 

579 

335241 

194104539 

24.0624 

8.3348 

515 

265225 

136590875 

22.6936 

8.0156 

580 

336400 

195112000 

24.0832 

S.3396 

516 

266256 

137388096 

22.7156 

8.0208 

581 

337561 

196122941 

24.1039 

8.3443 

517 

267289 

138188413 

22.7376 

8.0260 

588 

338724 

197137368 

24.1247 

8.3491 

518 

268324 

138991832 

22.7596 

8.0311 

583 

339889 

198155287 

24.1454 

8.3539 

519 

269361 

139798359 

22.7816 

8.0363 

584 

341056 

199176704 

24.1661 

8.3587 

520 

270400 

140608000 

22.8035 

8.0415 

585 

342225 

200201625 

24.1868 

8.3634 

521 

271441 

41420761 

22.8254 

8.0466 

586 

34339B 

201230056 

24.2074 

8.3682 

522 

272484 

42236648 

22.8473 

8.0517 

587 

344369 

202262003 

24.2281 

8.3730 

523 

273529 

43055667 

22.8692 

8.0569 

588 

345744 

203297472 

24.2487 

8.3777 

524 

274576 

43877824 

22.8910 

8.0620 

589 

346921 

204336469 

24.2693 

8.3*25 

525 

275625 

44703125 

22.9129 

8.0671 

590 

348100 

205379000 

24.2899 

8.3872 

526 

276676 

45531576 

22.9347 

8.0723 

591 

349281 

206423071 

24.3105 

8.3919 

527 

277729 

4636318: 

22.9565 

8.0774 

592 

350464 

207474688 

24.3311 

8.3967 

528 

278784 

47197952 

22.9783 

8.0825 

593 

351649 

208527857 

24.3516 

8.4014 

529 

279841 

48035889 

23.   ' 

8.0876 

594 

352836 

209584584 

24.3721 

8.4061 

330 

280  WO 

148877000 

23.0217 

8.0927 

593 

354023 

210644875 

24.892*i 

8.4103 

531 

281961  * 

149721291 

23.0134 

8.0978 

596 

355216 

211708736 

24.4131 

8.4155 

532 

283024 

150568768 

23.0651 

8.1028 

597 

356409 

212776173 

24.4336 

8.4202 

533 

284089 

151419437 

23.0868 

8.1079 

598 

857604 

213847192 

24.4540 

8.4249" 

534 

285156 

152273304 

23.10X4 

8.1130 

599 

358801 

214921799 

24.4745 

8.4296 

535 

286225 

153130375 

23.1301 

8.1180 

600 

360000 

216000000 

24.4949 

8.4343 

536 

287296 

153990656 

23.1517 

8.1231 

601 

361201 

217081801 

24.5153 

8.4390 

537 

288369 

154854153 

23.1733 

8.1281 

602 

362404 

218167208 

24.5357 

».  4437 

538 

289444 

155720872 

23.1948 

8.1332 

603 

363609 

219256227 

24.55bl 

8.4484 

539 

290521 

156590819 

23.21(54 

8.1382 

604 

364616 

220348864 

24.5764 

8.4530 

540 

291600 

157464000 

23.2379 

8.1433 

<i05 

366023 

221445125 

24.5967 

8.4577 

541 

292681 

158340421 

23.2594 

8.1483 

606 

367236 

222545016 

24.6171 

8.4623 

542 

293764 

159220088 

23.2809 

8.1533 

607 

368449 

223648543 

24.6374 

8.4870 

543 

294849 

160103007 

23.3024 

8.1383 

608 

369664 

224755712 

24.6577 

8.4716 

544 

295936 

160989184 

23.3238 

8.1633 

609 

370881 

2-.'X;»M:_'!-i 

-24.6779 

8.4763 

545 

297025 

161878625 

23.3452 

8.1683 

610 

372100 

226981000 

24.69S2 

8.4809 

546 

298116 

162771336 

23.3666 

8.1733 

611 

373321 

228099131 

24.7184 

8.4856 

547 

299209 

163667323 

23.3880 

8.1783 

612 

374544 

229220928 

24.7383 

8.4902 

548 

300304 

164566592 

23.4094 

8.1833 

613 

375769 

2:JO:U«:597 

24.7588 

8.494  •) 

549 

301401 

165469149 

23.4307 

8.1882 

614 

37»W96 

231475544 

24.7790 

8.4994 

550 

302500 

166375000 

23.4521 

8.1932 

615 

37*225 

23260*5375 

24.7992 

8.5340 

551 

303601 

167284151 

23.4734 

8.1982 

616 

379456 

23374439H 

24.8193 

8.5086 

552 

304704 

168196608 

23.4947 

8.2031 

617 

380689 

234885113 

24.8395 

8.5132 

553 

305809 

169112377 

23.5160 

8.2081 

618 

381924 

236029032 

24  85% 

8.5178 

554 

306916 

170031464 

23.5372 

8.2130 

619 

383161 

237176659 

24.8797 

8.  '5224 

555 

308025 

170953875 

23.5584 

8.2180 

620 

384400 

238328000 

24.8998 

8.5270 

556 

309136 

171879616 

2».  5797 

8.2229 

621 

385641 

239483061 

24.9199 

8.~5316 

557 

310249 

172808693 

23.6008 

8.2278 

622 

386884 

24064184* 

24.9399 

8.5362 

558 

311364 

173741112 

23.6220 

8.2327 

623 

388129 

241804367 

24.9600 

.  8.5408 

559 

312481 

174676879 

23.6432 

8.2377 

624 

3*9376 

242970624 

24.9800 

8.5453 

560 

313600 

175616000 

23.6643 

8.2426 

625 

390625 

244140625 

2& 

8.5499 

561 

314721 

176558481 

23.6854 

8.2475 

626 

391876 

245314376 

25.0200 

8.5544 

562 

315844 

177504328 

23.7065 

8.2524 

627 

393129 

246491883 

25.0400 

i?.5590 

563 

316969 

178453547 

23.7276 

8.2573 

628 

391384 

247673152 

25.0599 

8.5835 

564 

318096 

179406144 

23.7487 

8  2621 

629 

395641 

24885818» 

25.0799 

8.5681 

565 

319225 

180361U25 

23.7697 

8.2670 

630 

396900 

250047000 

25.0998  I 

S.57.'« 

566 

320356 

181321496 

23.7908 

8.2719 

631 

398161 

251239591 

25.1197 

8.577* 

567 

321489 

182284263 

23.8118 

8.2768 

632 

3994  _'4 

23213596.S 

25.1396 

g!58i7 

568 

322624 

183250432 

23.8328 

8.2816 

633 

4006H9 

•j.v,6:5«i::7 

25.1593 

*.5sH:i 

569 

323761 

184220009 

23.8537 

8.2865 

634 

401956 

2.-->  4*40104 

25.  1794 

£.51*07 

570 

324900 

185193000 

23.8747 

8.2913 

635 

403225 

256047.S75, 

25.DWJ 

8.5958 

571 

326041 

186169411 

23.8956 

8.2962 

(536 

40  UM 

257259456' 

25.2190  : 

8.5997 

572 

327184 

187149248 

23.9165 

8.3010 

«;{? 

4()5761» 

258474853 

25.23M9  • 

8.6043 

573 

32aS29 

188132517 

23.9374 

8.305M 

63S 

407014 

2596:^4072 

25.25X7 

S.«H3 

574 
675 

329476 
330625 

189119224 

i<K>io<m.'> 

23.»:>83 
28.979-2 

8.3107 
.  8  ..'ll-vS 

639 

408321 

4.n<*uxi 

2«0i>l71l9 
•>«•'  1  i4<M)0 

25.-J7S4 
•25  ••y*-' 

8.613U 
S.tilTT 

TAHLE  NO.  75-COK.  189 

From  Trautwine'*  "Civil  Engineer's  Pocket  Book.9* 


SQUARES,  CUBES,  AXD  ROOTS. 


TABLE  of  Squares,  4'uhes.  Square  Roots,  and  Cube  Roots, 
of  Numbers  from  1  to  1OOO  —  (CONTINUED.) 

No. 

Square. 

Cube. 

Sq.  Rt. 

C.  Rt 

No.  Square. 

Cube.   Sq.  Rt.   C.  Rt. 

251 
252 

63001 
63504 

15X13251 
1600300X 

15.8430 
15.8745 

•.8030 

6.3164 

316 
317 

99X56 
100488 

31554496 
31855018 

17.7764 
17.8045 

6.8113 
6.8185 

253 

64009 

16194277 

15.9060 

6.3217 

318 

101124 

32157432 

17.8326 

6.8256 

154 

64516 

16387064 

15.9374 

6.3330 

319 

101761 

32461759 

17.8606 

6.8328 

255 

65025 

16581375 

15.9687 

6.3413 

320 

102400 

32768000 

17.8885 

6.8399 

256 

65536 

16777216 

16. 

6.3496 

321 

103041 

33076161 

17.9165 

6.*470 

257 

66049 

16974593 

16.0312 

6.3579 

:vJ2 

103684 

33386248 

17.9444 

6.8541 

258 

66564 

17173512 

16.0834 

6.3661 

323 

104329 

33698267 

17.9722 

6.XH12 

259 

67681 

1  7373979 

1H.0935 

6.3743 

324 

104976 

34012224 

18. 

6.*(>-<3 

260 

67600 

17576000 

16.1245 

6.3X25 

325 

105625 

34328125 

18.0278 

6.8753 

261 

nan 

177795*1 

16.1555 

6.3907 

32(5    106276 

34645976 

18.0555 

6.8824 

262 

6*6  i  t 

I7:HH2> 

16.1864 

6.39x^ 

327    10«;>-'9 

34965783 

18.0831 

6.8894 

169 

69169 

18191447 

it;.  21  7:1 

6.4070 

328    107584 

35287552 

18.1108 

6.8964 

264 

«9fi% 

18399741 

16.2481 

6.4151 

329    108241 

35611289 

18.1384 

6.9034 

265 

70225 

18609625 

16.2788 

6.4232 

330    108900 

35937000 

18.1659 

6.9104 

166 

70756 

1XH21096 

16.3095 

6.4312 

331  i  109561 

36264691 

18.1934 

6.9174 

267 

71389 

19034163 

16.3401 

6.43113 

u:;_'   110224 

36594368 

18.2209 

6.9244 

m 

19248832 

16.3707 

6.4473 

333  |  110889 

36926037 

18.2483 

6.9313 

269 

72361 

19465109 

16.4012 

6.4553 

334  !  111556 

37259704 

18.2757 

6.9382 

270 

72900 

19683000 

16.4317 

6.4633 

335 

112225 

37595375 

18.3030 

6.9451 

271 

734*1 

19902511 

16.4621 

6.4713 

336 

112896 

37933056 

18.3303 

6.9521 

272 

73984 

2012364X 

16.4924 

6.4792 

337    113569 

38272753 

18.3576 

6.9589 

MS 

74529 

20346417 

16.5227 

6.4872 

338  i  114244 

38614472 

18.3848 

6.9658 

274 

75076 

20570824 

16.5529 

6.4951 

339   114921 

38958219 

18.4120 

6.9727 

275 

75625 

20796875 

16.5831 

6.5030 

340 

115600 

39304000 

18.4391 

6.9795 

276 

76176 

21024576 

16.6132 

6.5108 

341 

116281 

39651821 

18.4662 

6.9864 

277 

76729 

21253933 

16.6433 

6.5187 

342 

116964 

40001688 

18.4932 

6.9932 

278 

77384 

21484952 

16.6733 

6.5265 

343 

117649 

40353607 

18.5203 

7. 

279 

77841 

21717639 

16.7033 

6.5343 

344 

118336 

40707584 

18.5472 

7.0068 

280 

78400 

21952000 

16.7332 

6.5421 

345 

119025 

41063625 

18.5742 

7.0136 

Ml 

7X961 

22188041 

16.7631 

6.5499 

346 

119716 

41421736 

18.6011 

*  7.0203 

282 

79524 

22425768 

16.7929    6.5577 

347 

120409 

41781923 

18.6279 

7.0271 

H0089 

22665187 

6.8226     6.5654 

348 

121104 

42144192 

18.6548 

7.0338 

284 

X0f>56 

2290830* 

6.8523 

6.5731 

349 

121801 

42508549 

18.6815 

7.0406 

285 

81225 

23149125 

6.8819 

6.5808 

350 

122500 

42875000 

18.7083 

7.0473 

286 

81796 

23393656 

6.9115 

6.5885 

351 

123201 

43243551 

18.7350 

7.0540 

287 

X2369 

23639303 

6.9411 

6.5962 

352 

123904 

43614208 

18.7617 

7.0607 

288 

82M4 

23887872 

6.9708 

6.6039 

353 

124609 

43986977 

18.7883 

7.0674 

888 

83521 

24137569 

6.6115 

354 

125316 

44361864 

18.8149 

7.0740 

xoo 

84100 

24389000 

7^0294 

6.6191 

355 

126025 

44738875 

18.8414 

7.0807 

291 

84681 

24642171 

7.0587 

6.6267 

356 

126736 

45118016 

18.8680 

7.0873 

292 

85264 

248970X8 

7.0880 

6.6343 

357 

127449 

45499293 

18.8944 

7.0940 

3M 

85849 

25153757 

7.1172 

6.6419 

358 

128164 

45882712 

18.9209 

7.1006 

294 

«6«6 

25  U  21*4 

7.1464 

6.6494 

359 

128881 

46268279 

18.9473 

7.1072 

295 

87025 

•25672375 

7.1756 

6.6569 

360 

129600 

46656000 

18.9737 

7.1138 

296 

87616 

2593433* 

7.2047 

6.6644 

361 

130321 

47045881 

19. 

7.1204 

297 

88209 

26198073 

7.2337 

6.6719 

362 

131044 

47437928 

19.0263 

7.1269 

398 

88804 

2646:1592 

7.2627 

6.6794 

363 

131769 

47832147 

19.0526 

7.1335 

299 

89401 

26730899 

7.2i)16 

6.6869 

364 

1324% 

48228544 

19.0788 

7.1400 

300 

90000 

27000000 

7.3205 

6*6943 

365 

133225 

48627125 

19.1050 

7.1466 

301 

90601 

27270901 

7.3494 

6.7018 

366 

133956 

49027896 

19.1311 

7.1531 

302 

91204 

27543608 

7.3781 

6.7092 

367 

134689   49430863 

19.1572 

7.1596 

303 

91X09 

27818127 

7.4069 

6.7166 

368 

135424  !  49836032 

19.1833 

7.1661 

304 

92416 

2X094464 

7.4356 

6.7240 

369 

136161   50243409 

19.2094 

7.1726 

305 

93025 

28372625 

7.4642 

6.7313 

370 

136900 

50653000 

19.2354 

7.1791 

306 

93636 

28652616 

7.4929    6.7387 

371 

137641 

51064811 

19.2614 

7.1855 

307 

94249 

2X934443 

7.5214  !   6.7460 

372 

138384 

51478848 

19.2873 

7.1920 

308 

94864 

29218112 

7.5499    6.7533 

373 

139129 

51895117 

19.3132 

7.1984 

30?) 

95481 

29503629 

7.5784.    6.7606 

374 

139876 

52313624 

19.3391 

7.2043 

310 

96100 

29791000 

7.6068  :   6.7K79 

375 

140625 

52734375 

19.3649 

7.2112 

311 

96721 

300X0231 

7.IB52     6.7752 

376 

41376 

53157376 

19.3907 

7.2177 

312 

97344 

30371328 

7.6635     6.7824 

377 

42129 

535X2633 

19.4165 

7.2240 

313 

97969 

30664297 

7.6918 

6.7897 

378 

42-W4 

54010152 

19.4422 

7.2304 

314 

98596 

30959144 

7.7200 

6.7'W>9 

379 

43641 

54439939 

19.4679 

7.236* 

J15 

992*3 

31255875 

7.74>V^     6.8041 

3*0 

44400 

54372000 

19.4936    7.2431 

190  TBALE  NO.  75-CON. 

From  Trautwine's  "Civil  Engineer's  Pocket  Book." 


SQUARES,  CUBES,  AND  ROOTS. 

TABLE  of  Squares,  Cubes,  Square  Roots,  and  Cube  Roots, 
of  Numbers  from  1  to  1OOO  — (CONTINUED.) 


No. 

Square. 

Cube. 

Sq.  Rt. 

C.  Rt. 

No. 

Square. 

Cube. 

Sq.  Rt. 

C.  Rt. 

381 

382 

145161 
145924 

55306341 
55742968 

19.5192 
19.5448 

7.2495 
7.2558 

446 
447 

198916 
199809 

88716536 
89314623 

21.1187 
21.1424 

7.6403 
7.6460 

383 

146689 

56181887 

19.5704 

7.2622 

448 

200704 

89915392 

21.1660 

7.6517 

384 

147456 

56623104 

19.5959 

7.2685 

449 

201601 

90518849 

21.1896 

7.6574 

385 

148225 

57066625 

19.6214 

7.2748 

450 

202500 

91125000 

21.2132 

7.6631 

386 

148996 

57512456 

19.6469 

7.2811 

451 

203401 

91733851 

21.2368 

7.6688 

387 

149769 

57960603 

19.6723 

7.2874 

452 

204304 

92345408 

21.2603 

7.6744 

388 

150544 

58411072 

19.6977 

7.2936 

453 

205209 

92959677 

21.2838 

7.6801 

389 

151321 

58863869 

19.7231 

7.2999 

454 

206116 

93576664 

21.3073 

7.6857 

390 

152100 

59319000 

19.7484 

7.3061 

455 

207025 

94196375 

21.3307 

7.6914 

391 

152881 

59776471 

19.7737 

7.3124 

456 

207936 

94818816 

21.3542 

7.6970 

392 

153664 

60236288 

19.7990 

7.3186 

457 

208849 

95443993 

21.3776 

7.7026 

393 

154449 

60698457 

19.8242 

7.3248 

458 

209764 

96071912 

21.4009 

7.7082 

394 

155236 

61162984 

19.8494 

7.3310 

459 

210681 

96702579 

21.4243 

7.7138 

395 

156025 

61629875 

19.8746 

7.3372 

460 

211600 

97336000 

21.4476 

7.7194 

396 

156816 

62099136 

19.8997 

7.3434 

461 

212521 

97972181 

21.4709 

7.7250 

397 

157609 

62570773 

19.9249 

7.3496 

462 

213444 

98611128 

21.4942 

7.7306 

398 

158404 

63044792 

19.9499 

7.3558 

463 

214369 

99252847 

21.5174 

7.7362 

399 

159201 

63521199 

19.9750 

7.3619 

464 

215296 

99897344 

21.5407 

7.7418 

400 

160000 

64000000 

20. 

7.3681 

465 

216225 

100544625 

21.5639 

7.7473 

401 

160801 

64481201 

20.0250 

7.3742 

466 

217156 

101194696 

21.5870 

7.7529 

402 

161604 

64964808 

20.0499 

7.3803 

467 

218089 

101847563 

21.6102 

7.7584 

403 

162409 

65450827 

20.0749 

7.3864 

468 

219024 

102503232 

21.6333 

7.7639 

404 

163216 

65939264 

20.0998 

7.3925 

469 

219961 

103161709 

21.6564 

7.7695 

405 

164025 

66430125 

20.1246 

7.3986 

470 

220900 

103823000 

21.6795 

7.7750 

406 

164836 

66923416 

20.1494 

7.4047 

471 

221841 

104487111 

21.7025 

7.780S 

407 

165649 

67419143 

20.1742 

7.4108 

472 

222784 

105154048   21.7256 

7.786d 

408 

166464 

67917312 

20.1990 

7.4169 

473 

223729 

105823817 

21.7486 

7.7915 

409 

167281 

68417929 

20.2237 

7.4229 

474 

224676 

1  06496  424 

21.7715 

7.7970 

410 

168100 

68921000 

20.2485 

7.4290 

475 

225625 

107171875 

21.7945 

7.8025 

411 

168921 

69426531 

20.2731 

7.4350 

476 

226576 

107850176 

21.8174 

7.8079 

412 

169744 

69934528 

20.2978 

7.4410 

477 

227529 

108531333 

21.8403 

7.8134 

413 

170569 

70444997 

20.3224 

7.4470 

478 

228484 

109215352 

21.8632 

7.8188 

414 

171396 

70957944 

20.3470 

7.4530 

479 

229441    1  03902239 

21.8861 

7.8243 

415 

172225 

71473375 

20.3715 

7.4590 

480 

230400 

110592000 

21.9089 

7.8297 

416 

173056 

71991296 

20.3961 

7.4650 

481 

231361 

111284641 

21.9317 

7.8352 

417 

173889 

72511713 

20.4206 

7.4710 

482 

232324 

111980168 

21.9545 

7.8406 

418 

174724 

73034632 

20.4450 

7.4770 

483 

233289 

112678587 

21.9773 

7.8460 

419 

175561 

73560059 

20.4695 

7.4829 

484 

234256 

113379904 

22. 

7.8514 

420 

176400 

74088000 

20.4939 

7.4889 

485 

235225 

114084125 

22.0227 

7.8568 

421 

177241 

74618461 

20.5183 

7.4948 

486 

2361% 

114791256 

22.0454 

7.8622 

422 

178084 

75151448 

20.5426 

7.5007 

487 

237169 

115501303 

22.0681 

7.8676 

423 

178929 

75686967 

20.5670 

7.5067 

488 

238144 

116214272 

22.0907 

7.8730 

424 

179776 

76225024 

20.5913 

7.5126 

489 

239121 

116930169 

22.1133 

7.8784 

425 

180625 

76765625 

20.6155 

7.5185 

490 

240100 

117649000 

22.1359 

7.8837 

426 

181476 

77308776 

20.6398 

7.5244 

491 

241081 

118370771 

22.1585 

7.8891 

427 

182329 

77854483 

20.6640 

7.5302 

492 

242064 

119095488 

22.1811 

7.8944 

428 

183184 

78402752 

20.6882 

7.5361 

493 

243049 

119823157 

22.2036 

7.8998 

429 

184041 

78953589 

20.7123 

7.5420 

494 

244036 

120553784 

22.2261 

7.9051 

430 

184900 

79507000 

20.7364 

7.5478 

495 

245025 

121287375 

22.2486 

7.9105 

431 

185761 

80062991 

20.7605 

7.5537 

4% 

246016 

122023936 

22.2711 

7.9158 

432 

186624 

80621568 

20.7846 

7.5595 

497 

247009 

1227G3473 

22.2935 

7.9211 

433 

187489 

81182737 

20.8087 

7.5654 

498 

248004 

123505932 

22.3159 

7.9264 

434 

188356 

81746504 

20.8327 

7.5712 

499 

249001 

124251499 

22.3383 

7.9317 

435 

189225 

82312875 

20.8567 

7.5770 

500 

250000 

125000000 

22.3607 

7.9370 

436 

190096 

82881856 

20.8806 

7.5828 

501 

251001 

125751501 

22.3830 

7.942$ 

437 

190969 

83453453 

20.9045 

7.5886 

502 

252004 

126506008 

22.4054 

7.9476 

438 

191844 

84027672 

20.9284 

7.5944 

503 

253009 

127263527 

22.4277 

7.9528 

439 

192721 

84604519 

20.9523 

7.6001 

504 

254016 

128024064 

22.4499 

7.9581 

440 

193600 

85184000 

20.9762 

7.6059 

505 

255025 

128787625 

22.4722 

7.9634 

441 

194481 

85766121 

21. 

7.6117 

506 

256036 

129554216 

22.4944 

7.9686 

442 

195364 

86350888 

21.0238 

7.6174 

507 

257049 

130323843 

22.5167 

7.9739 

443 

196249 

86938307 

21.0476 

7.6232 

508 

258064 

131096512 

22.5389 

7.9791 

444 

197136 

87528384 

21.0713 

7.6289 

509 

259081 

131872229 

22.5610 

7.9843 

445 

196025 

88121125 

21.0950 

7.6346 

510 

260100 

132651000 

22.5832 

7.989* 

TABLE  NO.  75-CON.  191 

From  Traut  wine's  "•Civil  Engineer**  Pocket  Book." 


SQUARES,  CUBES,  AND   ROOTS. 

TABLE  of  Squares,  Cubes,  Square  Roots,  and  Cube  Roots, 
of  X  timbers  from  1  to  10OO  —  (CONTINUED.) 


Square. 

Cube. 

Sq.  Rt. 

C.  Rt. 

No. 

Square. 

Cube. 

Sq.  Rt. 

C.  Rt. 

410881 

263374721 

25.3180 

8.6222 

706 

498436 

351895*16 

26.5707 

8.9043 

412164 

264609288 

25.3377 

8.6267 

707 

499849 

353393243 

26.5895 

8.9085 

41.  'ill') 

265847707 

25.3574 

8.6312 

708 

501264 

354894912 

26.6083 

8.9127 

414736 

2670*99*4 

25.3772 

8.6357 

709 

5026*1 

3564008-29 

26.6271 

8.9169 

416025 

268336125 

25.3969 

8.6401 

710 

504100 

357911000 

26.6458 

8.9211 

41  73  16 

269586136 

25.4165 

8.6446 

711 

505521 

359425431 

26.6646 

8.9253 

418609 

270840023 

25.4362 

8.6490 

712 

506944 

360944128 

26.6833 

8.9295 

419304 

272097792 

25.4558 

8.6535 

713 

508369 

362467097 

26.7021 

8.9337 

421201 

27:W5:U49 

25.4755 

8.6579 

714 

509796 

363994344 

26.7208 

8,9378 

422500 

274625000 

25.4951 

8.6624 

715 

511225 

365525875 

26.7395 

8.942C 

423801 

275894451 

25.5147 

8.6668 

716 

512656 

367061696 

26.7582 

8.9462 

425104 

277167808 

25.5343 

8.6713 

717 

514089 

368601813 

26.7769 

8.9503 

426409 

278445077 

25.5539 

8.6757 

718 

515524 

370146232 

26.7955 

8.9545 

427716 

27972IW64 

25.5734 

8.6801 

719 

516961 

371694959 

26.8142 

8.9587 

429025 

281011375 

25.5930 

8.6845 

720 

518400 

373248000 

26.8328 

8.9628 

430336 

282300416 

25.6125 

8.6890 

721 

519841 

374805361 

26.8514 

8.%70 

4;n<U9 

2.«>35!U-593 

25.6320 

8.693-4 

722 

521284 

376367048 

26.8701 

8.9711 

4:i2yt>4 

284890312 

25.6515 

8.6978 

723 

522729 

377933067 

26.8887 

8.9752 

434281 

286191179 

25.6710 

8.7022 

724 

524176 

379503424 

26.9072 

8.9794 

435600 

287496000 

25.6905 

8.7066 

725 

525625 

381078125 

26.9258 

8.9835 

436921 

288804781 

25.7099 

8.7110 

726 

527076 

382657176 

26.9444 

8.9876 

4389*4 

290117528 

25.7294 

8.7154 

727 

528529 

384240583 

26.9629 

8.9918 

439569 

291434247 

25.7488 

8.7198 

728 

529984 

385828352 

26.9815 

8.9959 

440896 

292754944 

25.7682 

8.7241 

729 

531441 

387420489 

27. 

9. 

442225 

294079625 

25.7876 

8.7285 

730 

532900 

389017000 

27.0185 

9.0041 

443556 

295408296 

25.8070 

8.7329 

731 

534361 

390617891 

27.0370 

9.0082 

444889 

296740963 

25.8263 

8.7373 

732 

535824 

392223168 

27.0555 

9.0123 

446224 

298077632 

25.8457 

8.7416 

733 

537289 

393832837 

27.0740 

9.0164 

447i61 

299418309 

25.8650 

8.7460 

734 

538756 

395446904 

27.0924 

9.0205 

448900 

300763000 

25.8844 

8.7503 

735 

540225 

397065375 

27.1109 

9.0246 

450241 

302111711 

25.9037 

8.7547 

736 

541696 

398688256 

27.1293 

9.02*7 

45  1584 

303464448 

25.9230 

8.7590 

737 

543169 

400315553 

27.1477 

9.0328 

452929 

304821217 

25.9422 

8.7634 

738 

544644 

401947272 

27.1662 

9.0369 

454276 

306182024 

25.9615 

8.7677 

739 

546121 

403583419 

27.18i6 

9.0410 

455625 

307546875 

25.9808 

8.7721 

740 

547600 

405224000 

27.2029 

9.0450 

456976 

308915776 

26. 

8.7764 

741 

5490S1 

406869021 

27.2213 

D.0491 

458329 

31028*733 

26.0192 

8.7807 

742 

550564 

408518488 

27.2397 

9.0532 

459684 

311665732 

26.0384 

8.7850 

743 

552049 

410172407 

27.2580 

9.0572 

461041 

313046839 

26.0576 

8.7893 

744 

553536 

>  411830784 

27.2764 

9.0613 

462400 

314432000 

26.0768 

8.7937 

745 

555025 

413493625 

27.2947 

9.0654 

463761 

315821241 

26.0960 

8.7980 

746 

556516 

415160936 

27.3130 

9.0694 

465124 

317214568 

26.1151 

8.8023 

747 

558009 

416832723 

27.3313 

9.0735 

466489 

318611987 

26.1343 

8.8066 

748 

559504 

418508992 

27.3496 

9.0775 

467*56 

320013504 

26.1534 

8.8109 

749 

561001 

420189749 

27.3679 

9.0816 

469225 

321419125 

26.1725 

8.8152 

750 

562500 

421875000 

27.3861 

9.0856 

705% 

322828856 

26.1916 

8.8194 

751 

564001 

423564751 

27.4044 

9.08% 

71969 

324242703 

26.2107 

8.8237 

752 

565504 

425259008 

27.4226 

9.0937 

73344 

325660672 

26.2298 

8.8280 

753 

567009 

426957777 

27.4408 

9.0977 

74721 

327082769 

26.2488 

8.8323 

754 

568516 

428661064 

27.4591 

9.1017 

76100 

328509000 

26.2679 

8.8366 

755 

570025 

430368875 

27.4773 

9.1057 

77481 

329939371 

26.2869 

8.8408 

756 

571536 

432081216 

27.4955 

9.1098 

78864 

331',73*88 

26.3059 

8.8451 

757 

573049 

433798093 

27  5136 

9.1138 

80249 

33f.812557 

26.3249 

8.8493 

758 

574564 

435519512 

27.5318 

9.1178 

481636 

3:C4255384 

26.3439 

8.8536 

759 

576081 

437245479 

27.5500 

9.1218 

483025 

^35702375 

26.3629 

8.8578 

760 

577600 

438976000 

27.5681 

9.1258 

484416 

337153536 

26.o818 

8.8621 

761 

579121 

440711031 

27.5862 

9.1298 

485809 

338608873 

26.  4008 

8.8663 

762 

580644 

442450728 

27.6043 

9.1338 

4*7204 

340068392 

26.4197 

8.8706 

763 

582169 

444194947 

27.6225 

9.1378 

4**«01 

341532099 

26.43*6 

8.8748 

764 

5836% 

445943744 

27.6405 

9.1418 

490000 

343000000 

26.4575 

8.8790 

765 

585225 

447697125 

27.6586 

9.1458 

4B1401 

344472101 

26.47f  ' 

8.8833 

766 

586756 

4494550% 

27.6767 

9.1498 

492804 

345948408 

26.4953 

8.8875 

767 

588289 

451217663 

27.6948 

9.1537 

49*203 

3  4742*927 

26.5141 

88917 

768 

539824 

452»84832 

27.7128 

9.1577 

4)5616 

348913664 

26.5330 

8.8959 

769 

591361 

454756609 

27.7308 

9.1617 

497026 

350402625 

26.5518 

8.9001 

770 

592900 

456533008 

27.7489 

9.1657 

192  TABLE  NO.  75-CON. 

From  Tra lit  wine's  "  Civil  Engineer's  Pocket  Hook." 


SQUARES,  CUBES,  AND  ROOTS. 

TABLE  of  Squares,  Cubes,  Square  Roots,  and  Cube  Roots, 
of  Numbers  from  1  to  1OOO  —  (CONTINUED.; 


1 

No. 

Square. 

Cube. 

Sq.  Rt. 

C.  Rt. 

No.  Square.  Cube.  I  Sq.  Rt. 

C.  Rt. 

1 

771 

594441 

458314011 

27.7669 

9.1696 

836   698896   5842770561  28.9137 

9.4204 

772 

595984 

460099648 

27.7849 

9.1736 

837  I  700569 

586376253!  28.9310 

9.4241 

773 

!  597529 

461889917 

27.8029 

9.1775 

838 

702244    588480472*  28.9482 

9.4279 

774 

1  599076 

463684824 

27.N209 

9.1815 

839 

703921   590589719   28.9655 

9.4316 

775 

600625 

465484375 

27.8388 

9.1855 

840 

705600 

592704000 

28.9828 

9.4354 

776 

1  602176 

467288576 

27.8568 

9.1894 

841 

707281 

594823321 

29. 

9.4391 

777 

603729 

469097433   27.8747 

9.1933 

842 

708964 

596947688 

29.0172 

9.442* 

778 

;  605284 

470910952 

27.8927 

9.1973 

843 

710649 

599077107 

29.0345 

9.4466 

779 

606841 

472729139 

27.9106 

9.2012 

844 

712336 

601211584 

29.051  7 

9.4503 

780 

608400 

474552000 

27.9285 

9.2052 

845 

714025 

603%!  125  j  29.0689 

9.4541 

781 

1  609961 

476379541   27.9464 

9.2091 

846 

715716 

605495736 

29.0861 

9.4578 

782 

611524 

478211  768   27.9643 

9.2130 

847 

717409 

607645423  1  29.1033 

9.4615 

783 

613089 

480048887 

27.9821 

9.2170 

848 

719104 

609800192   29.1204 

9.4652 

784 

614656 

481830  W4 

28. 

9.2209 

849 

720801 

611960049 

29.1376 

9.4690 

785 

,  616225 

483736625 

28.0179 

9.2248 

850 

722500 

614125000 

29.1548 

9.4727 

786 

6177% 

485587656 

28.0357 

9.2287 

851 

724201 

616295051 

29.1719 

9.4764 

787 

619369 

487443403 

28.0535 

9.2326 

852 

725904 

618470208 

291890 

9.4801 

788 

620944 

483303*72 

28.0713 

9.2365 

853 

727609 

620650477 

29.  20(52 

9.4838 

789 

622521 

491169069 

28.0891 

9.2404 

854 

729316 

622835864 

29.2233 

9.4875 

790 

624100 

493039000 

28.1069 

9.2443 

855 

731025 

625026375 

29.2404 

9.4912 

791 

625681 

494913671 

28.1247 

9.2482 

856 

732736 

627222016 

29.2575 

9.4949 

792 

627264 

496793088 

28.1425 

9.2521 

857 

734449 

629422793 

29.2746 

9.4986 

793 

628819 

498677257 

28.1603 

9.2560 

858 

736164 

631828712 

29.2916 

9.5023 

794 

630*36 

500566184 

28.1780 

9.2599 

859 

737881 

633839779 

29.3087 

9.5060 

795 

632025 

502459875 

28.1957 

9.2638 

860 

739600 

636056000 

29.3258 

9.5097 

796 

633616 

504358336 

28.2135 

9.2677 

861 

741321 

638277381 

29.3428 

9.5134 

797 

635209 

506261573 

28.2312 

9.2716 

862 

743044 

640503928 

29.3598 

9.5171 

798 

636804 

508169592 

28.2489 

9.2754 

863 

744769 

642735647 

29.3769 

9.5207 

799 

638401 

510082399 

28.2666 

9.2793 

864 

7464% 

644972544 

29.3939 

9.5244 

800 

640000 

512000000   28.2843 

9.2832 

865 

748225 

647214625 

29.4109 

9.5281 

801 

641601 

513922401   28.3019 

9.2870 

866 

749956 

6494618% 

29.4279 

9.5317 

802 

643204 

515849608 

28.3196 

9.2909 

867 

751689 

651714363 

29.4449 

9.5354 

803 

61480;) 

517781627 

28.3373 

9.2948 

868 

753424 

653972032 

29.4618 

9.5391 

804 

64H416 

519718464 

28.3549 

9.2986 

869 

755161 

656234909 

29.4788 

9.5427 

805 

648025 

521660125   28.3725 

9.3025 

810 

756900 

658503000 

29.4958 

9.5464 

806 

649636 

523606616   28.3901 

9.3063 

87,1 

758641 

660776311   29.5127 

9.5501 

807 

651249 

525557943 

28.4077 

9.3102 

872 

760384 

663054848 

29.5296 

9.5537 

808 

652864 

527514112 

28.4253 

9.3140 

873 

762129 

665338617 

29.5466 

9.5574 

809 

654481 

529475129J  28.4429 

9.3179 

874   763876 

667627624 

29.5635 

9.5610 

810 

656100 

531441000'  28.4605 

9.3217 

875  1  765625 

669921875 

29.5804 

9.5647 

811 

6')7721 

533411731:  28.4781 

9.3255 

876 

767376 

672221376 

29.5973 

9.5683 

812 

6VM41 

535387328'  28.4956 

9.3294 

877 

769129 

674526133 

29.6142 

9.5719 

813 

f,;;0lii9 

537367797   28.5132 

9.3332 

878 

770884 

676836152 

29.6311 

9.5756 

8H 

66>5:->6 

:>39353144:  28.5307 

9.3370 

879 

772641 

679151439 

29.6479 

9.5792 

815 

664225 

541343375   28.5482 

9.3408 

880 

774400 

681472000 

29.6648 

9.5828 

816 

665856 

543338496;  285657 

9.3447 

881 

776161 

6&3797841 

29.6816 

9.5865 

817 

667489 

545:  :>5  13   28.5832     9.3485 

882 

777924 

686128968 

29.6985 

9.5901 

818 

669124 

547343432'  28.6007 

9.3523 

883 

77%89 

688465387 

29.7153 

9.5937 

819 

670761 

,->i9;ry;jr>9  28.6182 

9.3561 

884 

781456 

690807104 

29.7321 

9.5973 

820 

672400 

551368000 

28.6356 

9.3599 

885 

783225 

693154125 

29.7489 

9.6010 

821 

674041  ' 

553387661 

28.6531 

9.3637 

886 

7849% 

695506456 

29.7658 

9.6046 

822 

675684 

555412248 

28.6705 

9.3675 

887 

786769 

697864103 

29.7825 

9.6082 

823 

677329 

557441767 

28.6880 

9.3713 

888 

788544 

700227072 

29.7993 

9.6118 

824 

678976  , 

559476224 

28.7054 

9.3751 

889 

790321 

702595369 

29.8161 

9.6154 

825 

680625 

561515625 

28.7228 

9.3789 

890 

792100 

704%9000 

29.8329 

9.6190 

826 

681276 

563559976 

28.7402 

9.3827 

891 

793881 

707347971 

29.84% 

9.6226 

827 

683929 

5656092H3 

28.7576 

9.3865 

892 

795664 

709732288 

29.8664 

9.6262 

82H 

685584 

567663552 

28.7750 

9.3902 

893 

797449 

712121957 

29.8831 

9.6298 

829 

687241 

569722789 

28.7924 

9.3940 

894 

799236 

7145169H4 

29.8998 

9.6334 

830 

688900 

571787000 

28.8097 

9.3978 

895 

801025 

716917375 

29.9166 

9.a-no 

831 

690561 

573856191 

28.8271 

9.4016 

896   802816 

719323136 

29.9333 

9.6406 

832 

692224 

575930368 

28.8444    9.4053 

897    804609 

721734273 

29.9500 

9.6442 

833 

693889 

578009587 

28.8617  :   9.4091 

898   806404 

724150792 

29.9666 

».6477 

834 

695556 

580093704 

•»791     9.4129 

899   808201 

726572699 

29.9833 

9.6513 

835 

697225 

582182875 

28.8964  >   9.4166 

900   810000   729000000   30.       9.654* 

TABLE  NO.  75-CONCL.  193 


From  Trantwine's  '•  Civil  Fii«iii«M'r*s  Pocket  Book." 

SQUARES,  CUBES,  AND  ROOTS. 

TABLE  of  Squares,  Cubes,  Square  Roots,  and  Cube  Roots, 
of  Numbers  from  1  to  1OOO  — (CONTINUED.) 


No. 

Square. 

Cube. 

Sq.  Rt. 

C.  Rt. 

No. 

Square. 

1 
Cube. 

Sq.  Rt. 

C.Rt. 

901 
902 

811801  i  731432701   30.0167 
813604  i  733870808   30.0333 

9.6585 
9.6620 

951 
952 

904401 
906304 

860085351 
862801408 

30.a383 
30.8545 

9.8339 
9.8374 

903 

815409 

73631432" 

30.0500 

9.6656 

953 

908209 

865523177 

30.8707 

9.8403 

904 

817216 

738763264 

30.0666 

9.6692 

954 

910116 

868250664 

30.8869 

9.8443 

905 

819025 

741217625 

30.0832 

9.6727 

955 

912025 

870983875 

30.9031 

9.847T 

906 

820836 

743677416 

30.0998 

9.6763 

956 

913936 

873722816 

30.9192 

9.8511 

907 

822649 

7t«14-.'Ki: 

30.1164 

9.6799 

957 

915849 

876467493 

30.9354 

9.8546 

908 

824464 

7  48613:51  •_ 

30.1330 

9.6834 

958 

917764 

879217912 

30.9516 

9.8580 

909 

82M&J 

7:>HKH2! 

30.1496 

9.6870 

959 

919681 

881974079 

30.9677 

9.8614 

910 

828100 

753571000 

30.1662 

9.6905 

960 

921600 

884736000 

30.9839 

9.8648 

911 

829921 

756058031 

30.1828 

9.6941 

961 

923521 

887503681 

31. 

9.8683 

912 

831744 

758.550528 

30.1993 

9.6976 

962 

925444 

890277128 

31.0161 

9.871T 

913 

833569 

761048497 

30.2159 

9.7012 

963 

927369 

893056347 

31.0322 

9.8751 

914 

8353%    763551944 

30.2324 

9.7047 

964 

929296 

895841344 

31.0483 

9.8785 

915 

837225  !  766060875 

30.2490 

9.7082 

965 

931225 

898632125 

31.0644 

9.8819 

916 

839056   768575296 

30.2655 

9.7118 

966 

933156   901428696 

31.0805 

9.8854 

917 

840889 

771095213 

30.2820 

9.7153 

967 

935089  i  904231063 

81.0966 

9.8888 

91* 

«4'-'724 

773620632 

30.2985 

9.7188 

968 

937024 

907039232 

31.1127 

9.8922 

919 

844561 

776151559 

30.3150 

9.7224 

969 

938961 

909853209 

31.1288 

9.8956 

9'20 

846400 

778688000 

30.3315 

9,7259 

970 

940900 

912673000 

31.1448 

9.8990 

921 

848241 

781229961 

30.3480 

9.7294 

971 

942841 

915498611 

31.1609 

9.9024 

922 

850084 

783777448 

30.3645 

9.7329 

972 

944784 

918330048 

31.1769 

9.9053 

923 

851929 

786330467 

30.3809 

9.7364 

973 

946729 

921167317 

31.1929 

9.9092 

924 

853776 

788889024 

30.3974 

9.7400 

974 

948676 

924010424 

31.2090 

9.9126 

925 

855625 

791453125 

30.4138 

9.7435 

975 

950625 

926859375 

31.2250 

9.9160 

926 

857476 

794022776 

30.4302 

9.7470 

976 

952576 

929714176 

31.2410 

9.9194 

927 

859329 

796597983 

30.4467 

9.7505 

977 

954529 

932574833 

31.2570 

9.9227 

928 

861184 

799178752 

30.4631 

9.7540 

978 

956484 

935441352 

31.2730 

9.9261 

929 

863041 

801765089 

30.4795 

9.7575 

979 

958441 

938313739 

31.2890 

9.9295 

930 

864900 

804357000 

30.4959 

9.7610 

980 

960400 

941192000 

31.3050 

9.9329 

931 

866T61 

806954491 

30.5123 

9.7645 

981 

962361 

944076141 

31.3209 

9.9363 

932 

868624 

809557568 

30.5287 

9.7680 

982 

964324 

946966168 

31.3369 

9.93% 

933 

870489 

812166237 

30.5450 

9.7715 

983 

966289 

949862087 

31.3528 

9.9430 

934 

872356 

814780504 

30.5614 

9.7750 

984 

968256 

952763904 

31.3688 

9.9464 

935 

874225 

817400375 

30.5778 

9.7785 

985 

970225 

955671625 

31.3847 

9.9497 

936 

876096 

820025856 

30.5941 

9.7819 

986 

972196 

958585256 

31.4006 

9.9531 

937 

877969 

822656953 

30.6105 

9.7854 

987 

974169 

961504803 

31.4166 

9.9565 

938 

879844 

825293672 

30.6268 

9.7889 

988 

976144 

964430272 

31.4325 

9.959$ 

939 

881721 

827936019 

30.6431 

9.7924 

989 

978121 

967361669 

31.4484 

9.9632 

940 

883600 

830584000 

30.6594 

9.7959 

990 

980100 

970299000 

31.4643 

9.9666 

941 

885481 

833237621 

30.6757 

9.7993 

991 

982081 

973242271 

31.4802 

9.9699 

942 

887364 

8358968*8 

30.6920 

9.8028 

992 

984064 

976191488 

31.4960 

9.9733 

943 

889249 

838561807 

30.7083 

9.8063 

993 

986049 

979146657 

31.5119 

9.9766 

944 

891136 

841232384 

30.7246 

9.8097 

994 

988036 

982107784 

31.5278 

9.9800 

945 

893025 

843908625 

30.7409 

9.8132 

995 

990025 

985074875 

31.5436 

9.9833 

946 

894916 

846590536 

30.7571 

9.8167 

996 

992016 

988047936 

31.5595 

99866 

947 

896809 

849278123 

30.7734 

9.8201 

997 

994009 

991026973 

31.5753 

9!9900 

948 

898704   851971392 

30.7896 

9.8236 

998 

996004 

994011992 

31.5911 

9.9933 

949 

900601 

854670349 

30.8058 

9.8270 

999 

998001 

997002999 

31.6070 

9.996T 

950 

902500 

857375000 

30.8221 

9.8305 

1000 

1000000 

1000000000 

31.6228 

10, 

To  find  the  square  or  cube  of  any  whole  number  ending1 
Mil li  ciphers.     First,  omit  all  the  final  ciphers.    Take  from  the  table  the 

square  or  cube  (as  the  case  may  be)  of  the  rest  of  the  number.  To  this  square  add  twice  as  many 
ciphers  as  there  were  final  ciphers  in  the  original  number.  To  the  cube  add  three  times  as  many  as 
in  the  original  number.  Thus,  for  905003;  9052  =  819025.  Add  twice  2  ciphers,  obtaining  8190250000. 
For  905003,  9053  =  741217625.  Add  i  times  2  ciphers,  obtaining  741217625000000. 


194  TABLE  NO.  76. 

From  Tra  lit  wine's  "Civil  Engineer's  Poeket  Book.9 

SQUARE  AND  CUBE  ROOTS. 


Square  Roots  and  Cube  Roots  of  Numbers  from  1OOO  to  1OOOO. 

No  errors. 


Num. 

Sq.  Rt. 

Cu.  Rt 

Num. 

Sq.  Rt. 

Cu.  Rt. 

Num. 

Sq.  Rt. 

Cu.  Rt. 

Num. 

Sq.  Rt. 

Cu.  Rt. 

1005 

31.70 

10.02 

1405 

37.48 

11.20 

1805 

42.49 

12.18 

2205 

46.96 

13.02 

1010 

31.78 

10.03 

1410 

37.55 

11.21 

1810 

42.54 

12.19 

2210 

47.01 

13.03 

1015 

31.86 

10.05 

1415 

37.62 

11.23 

1815 

42.60 

12.20 

2215 

47.06 

13.04 

1020 

31.94 

10.07 

1420 

37.68 

11.24 

1820 

2.66 

12.21 

2220 

47.12 

13.05 

1025 

32.02 

10.08 

1425 

37.75 

11.25 

1825 

2.72 

12.22 

2225 

47.17 

13.05 

1030 

32.09 

10.10 

1430 

37.82 

11.27 

1830 

2.78 

12.23 

2230 

47.22 

13.06 

1035 

32.17 

10.12 

1435 

37.88 

11.28 

1835 

2.84 

12.24 

2235 

47.28 

13.07 

1040 

32.25 

10.13 

1440 

37.95 

11.29 

1840 

2.90 

12.25 

2240 

47.33 

13.08 

1045 

32.33 

10.15 

1445 

38.01 

11.31 

1845 

2.95 

12.26 

2245 

47.38 

13.09 

1050 

32.40 

10.16 

1450 

38.08 

11.32 

1850 

3.01 

2.28 

2250 

47.43 

13.10 

1055 

32.48 

10.18 

1455 

38.14 

11.33 

1855 

43.07 

2.29 

2255 

47.49 

13.11 

1060 

32.56 

10.20 

1460 

38.21 

11.34 

1860 

3.13 

2.30 

2260 

47.54 

13.12 

1065 

32.63 

10.21 

1465 

38.28 

11.36 

1865 

43.19 

2.31 

2265 

47.59 

13.13 

1070 

32.71 

10.23 

1470 

38.34 

11.37 

1870 

43.24 

2.32 

2270 

47.64 

13.14 

1075 

32.79 

10.24 

1475 

38.41 

11.38 

1875 

43.30 

2.33 

2275 

47.70 

13.15 

1080 

32.86 

10.26 

1480 

38.47 

11.40 

1880 

43.36 

2.34 

2280 

47.75 

13.16 

1085 

32.94 

10.28 

1485 

38.54 

11.41 

1885 

43.42 

2.35 

2285 

47.80 

13.17 

1090 

33.02 

10.29 

1490 

38.60 

1.42 

1890 

43.47 

2.36 

2290 

47.85 

13.18 

1095 

33.09 

10.31 

1495 

38.67 

1.43 

1895 

43.53 

2.37 

2295 

47.91 

13.19 

1100 

33.17 

10.32 

1500 

38.73 

1.45 

1900 

43.59 

2.39 

2300 

47.% 

13.20 

1105 

33.24 

10.34 

1505 

38.79 

1.46 

1905 

43.65 

2.40 

2305 

48.01 

13.21 

1110 

33.32 

10.35 

1510 

38.86 

1.47 

1910 

43.70 

2.41 

2310 

48.06 

13.22 

1115 

33.39 

10.37 

1515 

38.92 

1.49 

1915 

43.76 

2.42 

2315 

48.11 

13.23 

1120 

33.47 

10.38 

1520 

38.99 

1.50 

1920 

43.82 

2.43 

2320 

48.17 

13.24 

1125 

33.54 

10.40 

1525 

39.05 

1.51 

1925 

43.87 

2.44 

2325 

48.22 

13.25 

1130 

33.62 

10.42 

1530 

39.12 

1.52 

1930 

43.93 

2.45 

2330 

48.27 

13.26 

1135 

33.69 

10.43 

1535 

39.18 

1.54 

1935 

43.99 

2.46 

2335 

48.32 

13.27 

1140 

33.76 

10.45 

1540 

39.24 

1940 

44.05 

2.47 

2340 

48-37 

13.28 

1145 

33.84 

10.46 

1545 

39.31 

l!56 

1945 

44.10 

2.48 

2345 

48.43 

13.29 

1150 

33.91 

10.48 

1550 

39.37 

1.57 

1950 

44.16 

2.49 

2350 

48.48 

13.80 

1155 

33.99 

10.49 

1555 

39.43 

1.59 

1955 

44.22 

2.50 

2355 

48.53 

13.30 

1160 

34.06 

10.51 

1560 

39.50 

1.60 

1960 

44.27 

2.51 

2360 

48.58 

13.31 

1165 

34.13 

10.52 

1565 

39.56 

1.61 

J965 

44.33 

2.53 

2365 

48.63 

13.32 

1170 

34.21 

10.54 

1570 

39.62 

1.62 

1970 

44.38 

2.54 

2370 

48.68 

13.33 

1175 

34.28 

10.55 

1575 

39.69 

1.63 

1975 

44.44 

2.55 

2375 

48.73 

13.34 

1180 

34.35 

10.57 

1580 

39.75 

1.65 

1980 

44.50 

2.56 

2380 

48.79 

13.35 

1185 

34.42 

10.58 

1585 

39.81 

1.66 

1985 

44.55 

2.57 

2385 

48.84 

13.36 

1190 

34.50 

10.60 

1590 

39.87 

1.67 

1990 

44.61 

2.58 

2390 

48.89 

13.37 

1195 

34.57 

10.61 

1595 

39.94 

1.68 

1995 

44.67 

2.59 

2395 

48.94 

13.38 

1200 

34.64 

10.63 

1600 

40.00 

1.70 

2000 

44.72 

2.60 

2400 

48.99 

13.39 

1205 

34.71 

10.64 

1605 

40.06 

1.71 

2005 

44.78 

2.61 

2405 

49.04 

13.40 

1210 

34.79 

10.66 

1610 

40.12 

1.72 

2010 

44.83 

2.62 

2410 

49.09 

13.41 

1215 

34.86 

10.67 

1615 

40.19 

1.73 

2015 

44.89 

2.63 

2415 

49.14 

13.42 

1220 

84.93 

10.69 

1620 

40.25 

1.74 

2020 

44.94 

2.64 

2420 

49.19 

13.43 

1225 

35.00 

10.70 

1625 

40.31 

1.76 

2025 

45.00 

2.65 

2425 

49.24 

13.43 

1230 

35.07 

10.71 

1630 

40.37 

1.77 

2030 

.  45.06 

2.66 

2430 

49.30 

13.44 

1235 

35.14 

10.73 

1635 

40.44 

1.78 

2035 

45.11 

2;  67 

2435 

49.35 

13.45 

1240 

35.21 

10.74 

1640 

40.50 

1.79 

2040 

45.17 

2.68 

2440 

49.40 

13.46 

1245 

35.28 

10.76 

1645 

40.56 

1.80 

2045 

45.22 

2.69 

2445 

49.45 

13.47 

1250 

35.36 

10.77 

1650 

40.62 

1.82 

2050 

45.28 

2.70 

2450 

49.50 

13.48 

1255 

35.43 

10.79 

1655 

4d.68 

1.83 

2055 

45.33 

2.71 

2460 

49.60 

13.50 

1260 

35.50 

10.80 

1660 

40.74 

1.84 

2060 

45.39 

2.72 

2470 

49.70 

13.52 

1265 

35.57 

10.82 

1665 

40.80 

1.85 

2065 

45.44 

12.73 

2480 

49.80 

13.54 

1270 

35.64 

10.83 

1670 

40.87 

1.8o 

2070 

45.50 

12.74 

2490 

49.90 

13.55 

1275 

35.71 

10.84 

1675 

40.93 

1.88 

2075 

45.55 

12.75 

2500 

50.00 

13.57 

1280 

35.78 

10.86 

1680 

40.99 

1.89 

2080 

4561 

12.77 

2510 

50.10 

13.59 

1285 

35.85 

10.87 

1685 

41.05 

1.90 

2085 

45.66 

12.78 

2520 

50.20 

13.61 

1290 

35.92 

10.89 

1690 

41.11 

1.91 

2090 

45.72 

12.79 

2530 

50.30 

13.63 

1295 

35.99 

10.90 

1695 

41.17 

1.92 

2095 

45.77 

12.80 

2540 

50.40 

13.64 

1300 

36.06 

10.91 

1700 

41.23 

11.93 

2100 

45.83 

12.81 

2550 

5050 

13.66 

1305 

36.12 

10.93 

1705 

41.29 

11.95 

2105 

45.88 

12.82 

2560 

50.60 

13.68 

1310 

36.19 

10.94 

1710 

41.35 

11.96 

2110 

45.93 

12.83 

2570 

50.70 

13.70 

1315 

86.26 

10.96 

1715 

41.41 

11.97 

2115 

45.99 

12.84 

2580 

50.79 

13.72 

1320 

86.33 

10.97 

1720 

41.47 

11.98 

2120 

46.04 

12.85 

2590 

50.89 

13.73 

1325 

36.40 

10.98 

1725 

41.53 

11.99 

2125 

46.10 

2.86 

2600 

50.99 

13.75 

1330 

36.47 

11.00 

1730 

41.59 

12.00 

2130 

46.15 

12.87 

2610 

51.09 

13.7T 

1335 

36.54 

11.01 

1735 

41.65 

12.02 

2135 

46.21 

12.88 

2620 

51.19 

13.79 

1340 

36.61 

11.02 

1740 

41.71 

12.03 

2140 

46.26 

2.89 

2630 

51.28 

13.80 

1345 

36.67 

11.04 

1745 

41.77 

12.04 

2145 

46.31 

2.90 

2640 

51.38 

13.82 

1350 

36.74 

11.05 

1750 

41.83 

12.05 

2150 

46.37 

2.91 

2650 

51.48 

13.84 

1355 

36.81 

11.07 

1755 

41.89 

12.06 

2155 

46.42 

2.92 

2660 

51.58 

13.86 

1360 

36.88 

11.08 

1760 

41.95 

12.07 

2160 

46.48 

2.93 

2670 

51.67 

13.8T 

1365 

36.95 

11.09 

1765 

42.01 

12.09 

2  65 

46.53 

12.94 

2680 

51.77 

13.89 

1370 

37.01 

11.11 

1770 

42.07 

12.10 

2  70 

46.58 

12.95 

2690 

51.87 

13.91 

1375 

37.08 

11.12 

1775 

42.13 

12.11 

2  75 

46.64 

12.96 

2700 

51.96 

13.92 

1380 

37.15 

11.18 

1780 

42.19 

12.12 

2  80 

46.69 

12.97 

2710 

52.06 

13.94 

1385 

37.22 

11.15 

1785 

42.25 

12.13 

2  85 

46.74 

12.98 

2720 

52.15 

13.96 

1390 

37.28 

11.16 

1790 

42.31 

12.14 

2  90 

46.80 

12.99 

2730 

52.25 

13.98 

1395 

37.35 

11.17 

1795 

42.37 

12.15 

2195 

46.85 

13.00 

2740 

52.35 

13.99 

1400 

37.42 

11.19 

1800 

42.43 

12.16 

2200 

46.80 

13.01 

2750 

52.44 

14.01 

TABLE  NO.  76— CON.  195 

From  Trautwine's  "Civil  Engineer's  Pocket  Book." 


SQUARE  AND  CUBE  ROOTS. 

Kquare  Roots  and  Cube  Roots  of  Numbers  from  1OOO  tolOOOO 

— (CONTINUED.) 


Num. 

Sq.  Rt. 

Cu.  Rt 

Num. 

Sq.  Rt. 

Cu.  Rt 

Num. 

Sq.  Rt. 

Cu.Rt 

Num. 

Sq.  Rt. 

Cu.  Rt. 

27(50 

52.54 

14.03 

3550 

59.58 

15.25 

4340 

65.88 

16.31 

5130 

71.62 

17.25 

2770 

52.63 

14.04 

3560 

59.67 

15.27 

4350 

65.95 

16.32 

5140 

71.69 

17.26 

2780 

52.73 

14.06 

3570 

59.75 

15.28 

4360 

66.03 

16.34 

5150 

71.76 

17.27 

2790 

52.82 

14.08 

3580 

59.83 

15.30 

4370 

66.11 

16.35 

5160 

71.83 

17.28 

2800 

52.92 

14.09 

3590 

59.92 

15.31 

4380 

66.18 

16.36 

5170 

71.90 

17.29 

2810 

53.01 

14.11 

3600 

60.00 

15.33 

4390 

66.26 

16.37 

5180 

71.97 

17.30 

2820 

53.10 

14.13 

3610 

60.08 

15.34 

4400 

66.33 

16.39 

5190 

72.04 

17.31 

2830 

53.20 

14.14 

3620 

60.17 

15.35 

4410 

66.41 

16.40 

5200 

72.11 

17.32 

2S40 

53.29 

14.16 

3630 

60.25 

15.37 

4420 

66.48 

16.41 

5210 

72.18 

17.34 

2850 

53.39 

14.18 

3640 

60.33 

15.38 

4430 

66.56 

1642 

5220 

72.25 

7.35 

2860 

53.48 

14.19 

3650 

60.42 

15.40 

4440 

66.63 

16.44 

5230 

72.32 

7.36 

2870 

53.57 

14.21 

3660 

60.50 

15.41 

4450 

66.71 

16.45 

5240 

72.39 

7.37 

2880 

53.67 

14.23 

3670 

60.58 

15.42 

4460 

66.78 

16.4« 

5250 

72.46 

7.38 

2890 

53.76 

14.24 

3680 

60.66 

15.44 

4470 

6686 

16.47 

5260 

72.53 

7.39 

2900 

53.85 

14.26 

3690 

60.75 

15.45 

4480 

66.93 

16.49 

5270 

72.59 

7.40 

2910 

53.94 

14.28 

3700 

CO.  83 

15.47 

4490 

67.01 

1650 

5280 

72.66 

7.41 

2920 

54.04 

14.29 

3710 

60.91 

15.48 

4500 

67.08 

1651 

5290 

72.73 

17.42 

2930 

54.13 

14.31 

3720 

60.99 

15.49 

4510 

67.16 

16.52 

5300 

72.80 

7.44 

2940 

54.22 

14.33 

3730 

61.07 

15.51 

4520 

67.23 

16.53 

5310 

72.87 

7.45 

2950 

54.31 

14.34 

3740 

61.16 

15.52 

4530 

67-31 

16.55 

5320 

72.94 

7.46 

2960 

54.41 

14.36 

3750 

61.24 

15.54 

4540 

67.38 

16.56 

5330 

73.01 

17.47 

2970 

54.50 

14.37 

3760 

61.32 

15.55 

4550 

67.45 

16.57 

5340 

73.08 

17.48 

2980 

54.59 

14.39 

3770 

61.40 

15.56 

4560 

67.53 

16.58 

5350 

73.14 

17.49 

2990 

54.68 

14.41 

3780 

61.48 

15.58 

4570 

67.60 

16.59 

5360 

73.21 

17.50 

3000 

54.77 

14.42 

3790 

61.56 

15.59 

4580 

67.68 

16.61 

5370 

73.28 

17.51 

3010 

54.86 

14.44 

3800 

6164 

15.  (50 

4590 

67.75 

16.62 

5380 

73.35 

17.52 

3020 

54.95 

14.45 

3810 

61.73 

15.62 

4600 

67.82 

16.63 

5390 

73.42 

17.53 

3030 

55.05 

14.47 

3820 

61.81 

15.63 

4610 

67.1-0 

1«.»>4 

5400 

73.48 

17.54 

3040 

55.14 

14.49 

3830 

61.89 

15.65 

46i:o 

67.97 

16.C6 

5410 

73.55 

7.55 

3050 

55.23 

14.50 

3840 

61.97 

15.66 

4630 

68.04 

16.67 

5420 

73.62 

7.57 

3060 

55.  32 

14.52 

3850 

62.05 

15.67 

4640 

68.12 

16.68 

5430 

73.69 

7.58 

3070 

55.41 

14.53 

3860 

62.13 

15.69 

4650 

68.19 

18.C9 

5440 

73.76 

7.59 

3080 

55.50 

14.55 

3870 

62.21 

15.70 

4660 

68.26 

16.70 

5450 

73.82 

7.60 

3090 

55.59 

14.57 

3880 

62.29 

15.71 

4670 

68.34 

16.71 

5460 

73.89 

7.61 

3100 

55.68 

14.58 

3890 

62.37 

15.73 

4680 

68.41 

16.73 

5470 

73.96 

7.62 

3110 

55.77 

14.60 

3900 

62.45 

15.74 

4690 

68.48 

16.74 

5480 

74.03 

7.63 

3120 

55.86 

14.61 

3910 

62.53 

15.75 

4700 

68  56 

16.75 

5490 

74.09 

7.64 

3130 

55.95 

14.63 

3920 

62.61 

15.77 

4710 

68.63 

16.76 

5500 

74.16 

17.65 

3140 

56.04 

14.64 

3930 

62.69 

15.78 

4720 

68.70 

16.77 

5510 

74.23 

17.66 

3150 

56.12 

14.66 

3940 

62.77 

15.79 

4730 

68.TT 

16.79 

5520 

74.30 

17.67 

3160 

56.21 

14.67 

3950 

62.85 

15.81 

4740 

68.85 

16.80 

.5530 

74.36 

17.68 

3170 

56.30 

14.69 

3960 

62.93 

15.82 

4750 

68.92 

16.81 

5540 

74.43 

17.69 

3180 

56.39 

14.71 

3970 

63.01 

15.83 

4760 

68.99 

16.82 

5550 

74.50 

17.71 

3190 

56.48 

14.72 

3980 

63.09 

15.85 

4770 

69.07 

16.83 

5560 

74.57 

17.72 

3200 

56.57 

14.74 

3990 

63.17 

15.86 

4780 

69.14 

16.85 

5570 

74.63 

17.73 

3210 

56,66 

14.75 

4000 

63.25 

15.87 

4790 

6921 

16.86 

5580 

74.70 

17.74 

3220 

56.75 

14.77 

4010 

63.32 

15.89 

4800 

69.28 

16.87 

5590 

74.77 

17.75 

3230 

56.83 

14.78 

4020 

63.40 

15.90 

4810 

69.35 

16.88 

5600 

74.83 

17.76 

3240 

56.92 

14.80 

4030 

63.48 

15.91 

4820 

69.43 

1689 

5610 

74.90 

17.77 

3250 

57.01 

14.81 

4040 

63.56 

15.93 

4830 

69.50 

16.90 

5620 

74.97 

17.78 

3260 

57.10 

14.83 

4050 

63.64 

15.94 

4840 

69.57 

16.92 

5630 

75.03 

17.79 

3270 

57.18 

14.£4 

4060 

63.72 

15.95 

4850 

69.64 

16.93 

5640 

75.10 

17.80 

3280 

57.27 

14.86 

4070 

63.80 

15.97 

4860 

69.71 

16.94 

5650 

75.17 

17.81 

3290 

57.36 

14.87 

4080 

63.87 

15.98 

4870 

69.79 

16.95 

5660 

75.23 

17.82 

3300 

57.45 

14.89 

4090 

63.95 

15.99 

4880 

69.86 

16.96 

5670 

75.30 

7.83 

3310 

57.53 

14.90 

4100 

64.03 

16.01 

4890 

69.93 

16.97 

5680 

75.37 

7.84 

3320 

57.62 

14.92 

4110 

64.11 

16.02 

4900 

70.00 

16.98 

5690 

75.43 

7.85 

3330 

57.71 

14.93 

4120 

64.19 

16.03 

4910 

70.07 

17.00 

5700 

75.50 

7.86 

3340 

57.79 

14.95 

4130 

64.27 

16.04 

4920 

70.14 

17.01 

5710 

75.56 

7.87 

3350 

57.88 

14.96 

4140 

64.34 

16.06 

4930 

70.21 

17.02 

5720 

75.63 

7.88 

3360 

57.97 

14.98 

4150 

64.42 

16.07 

4940 

70.29 

17.03 

5730 

75.70 

7.89 

3370 

58.05 

14.99 

4160 

64.50 

16.08 

4950 

70.36 

17.04 

5740 

75.76 

17.90 

3380 

58.14 

15,01 

4170 

64.58 

16.10 

4960 

70.43 

17.05 

5750 

75.83 

17.92 

3390 

58.22 

15.02 

4180 

64.65 

16.11 

4970 

70.50 

17.07 

5760 

75.89 

17.93 

3400 

58.31 

15.04 

4190 

64.73 

16.12 

4980 

70.57 

17.08 

5770 

75.96 

17.94 

3410 

58.40 

15.05 

4200 

64.81 

16.13 

4990 

70.64 

17.09 

5780 

76.03 

17.95 

3420 

58.48 

15.07 

4210 

64.88 

16.15 

5000 

70.71 

17.10 

5790 

76.09 

17.96 

3430 

58.57 

15.08 

4220 

64.96 

16.16 

5010 

70.78 

17.11 

5800 

76.16 

17.97 

3440 

58.65 

15.10 

4230 

65.04 

16.17 

5020 

70.85 

17.12 

5810 

76.22 

17.98 

3450 

58.74 

15.11 

4240 

65.12 

16.19 

5030 

70.92 

17.13 

5820 

76.29 

17.99 

3460 

58.82 

15.12 

4250 

65.19 

16,20 

5040 

70.99 

17.15 

5830 

76.35 

18.00 

3470 

58.91 

15.14 

4260 

65.27 

16.21 

5050 

71.06 

17.16 

5840 

76.42 

18.01 

3480 

58.99 

15.15 

4270 

65.35 

16.22 

5060 

71.13 

17.17 

5850 

76.49 

18.02 

3490 

59.08 

15.17 

4280 

65.42 

16.24 

5070 

71.20 

17.18 

5860 

76.55 

18.03 

3500 

59.16 

15.18 

4290 

65.50 

16.25 

5080 

71.27 

17.19 

5870 

76.62 

18.04 

3510 

59.25 

15.20 

4300 

6557 

16.26 

5090 

71.34 

17.20 

5880 

76.68 

18.05 

3520 

59.33 

15.21 

4310 

65.65 

16.27 

5100 

71.41 

17.21 

5890 

76.75 

18.06 

3530 

59.41 

15.23 

4320 

65.73 

16.29 

5110 

71.48 

17.22 

5900 

76.81 

18.07 

8640 

59.50 

15.24 

4330 

65.80 

16.30  1 

5120 

71.55 

17.24 

5910 

76.88 

18.08 

196  TABLE  NO.  76— COX. 

From  Train  wine's  •'  Civil  Engineer's  Pocket  Book.* 


SQUARE  AND  CUBE  ROOTS. 
Bqiiare  Roots  and  Cube  Roots  of  Numbers  from  1OOO  to  1OOOO 

—  (CONTINUED.) 


Num. 

Sq.  Rt.  Cu.  Rt. 

Num. 

Sq.  Rt. 

Cu.Rt. 

Num. 

Sq.  Rt. 

Cu.  Rt. 

Num.  |Sq.  Rt. 

Cu.Rt 

5920 

76.94 

18.09 

6710 

81.91 

18.86 

7500 

86.60 

19.57 

8290 

91.05 

20.24 

593C 

77.01 

18.10 

6720 

81.98 

18.87 

7510 

86.66 

19.58 

8300 

91.10 

20.25 

5940 

77.07 

18.11 

6730 

82.04 

18.88 

7520 

86.72 

19.59 

8310 

91.16 

20.26 

5950 

77.14 

18.12 

6740 

82.10 

18.89 

7530 

86.78 

19.60 

8320 

91.21 

20.26 

5960 

77.20 

18.13 

6750 

82.16 

18.90 

7540 

86.83 

19.61 

8330 

91.27 

20.27 

597G 

77.27 

18.14 

6760 

82.22 

18.91 

7550 

86.89 

19.62 

8340 

91.32 

20.28 

5980 

77.33 

18.15 

6770 

82.28 

18.92 

7560 

86.95 

19.63 

8350 

91.38 

20.29 

5990 

77.40 

18.16 

6780 

82.34 

18.93 

7570 

87.01 

19.64 

8360 

91.43 

20.30 

6000 

77.46 

18.17 

6790 

82.40 

18.94 

7580 

87.06 

19.64 

8370 

91.49 

20.30 

6010 

77.52 

18.18 

6800 

82.46 

18.95 

7590 

87.12 

19.65 

8380 

91.54 

20.31 

6020 

77.59 

18.19 

6810 

82.52 

18.95 

7600 

87.18 

19.66 

8390 

91.60 

20.32 

6030 

77.65 

18.20 

6820 

82.58 

18.96 

7610 

87.24 

19.67 

8400 

91.65 

20.33 

6040 

77.72 

18.21 

6830 

82.64 

18.97 

7620 

87.29 

19.68 

8410 

91.71 

20.34 

6050 

77.78 

18.22 

6840 

82.70 

18.98 

7630 

87.35 

19.69 

8420 

91.76 

20.34 

6060 

77.85 

18.23 

6850 

82.76 

18.99 

7640 

87.41 

19.70 

8430 

91.82 

20.35 

6070 

77.91 

18.24 

6860 

82.83 

19.00 

7650 

87.46 

19.70 

8440 

91.87 

20.36 

6080 

77.97 

8.25 

6870 

82.89 

19.01 

7660 

87.52 

19.71 

8450 

91.92 

20.37 

6090 

78.04. 

8.26 

6880 

82.95 

19.02 

7670 

87.58 

19.72 

8460 

91.98 

20.38 

6100 

78.10 

8.27 

6890 

83.01 

19.03 

7680 

87.64 

19.73 

8470 

92.03 

20.38 

6110  i  78.17 

8.28 

6900 

83.07 

19.04 

7690 

87.69 

19.74 

8480 

92.09 

20.39 

6120 

73.23 

8.29 

6910 

83.13 

19.05 

7700 

87.75 

19.75 

8490 

92.14 

20.40 

6130 

78.29 

8.30 

6920 

83.19 

19.06 

7710 

87.81 

19.76 

8500 

92.20 

20.41 

6140 

78.36 

8.31 

6930 

83.25 

19.07 

7720 

87.86 

19.76 

8510 

92.25 

20.42 

6150 

78.42 

8.32 

6940 

83.31 

19.07 

7730 

87.92 

19.77 

8520 

92.30 

20.42 

«160 

78.49 

8.33 

6950 

83.37 

19.08 

7740 

87.98 

19.78 

8530 

92.36  i  20.43 

6170 

78.55 

8.34 

6960 

83.43 

19.09 

7750 

88.03 

19.79 

8540 

92.41  i  20.44 

6180 

78.61 

8.35 

6970 

83.49 

19.10 

7760 

88.09 

9.80 

8550 

92.47 

20.45 

6190 

78.68 

8.36 

6980 

83.55 

19.11 

7770 

88.15 

9.81 

8560 

92.52 

20.46 

6200 

18.74 

8.37 

6990 

83.61 

19.12 

7780 

88.20 

9.81 

8570 

92.57 

20.46 

6210 

78.80 

8.38 

7000 

83.67 

19.13 

7790 

88.26 

9.82 

8580 

92.63 

20.47 

6220 

78.87 

8.39 

7010 

83.73 

19.14 

7800 

88.32 

9.83 

8590 

92.68 

20.48 

6230 

78.93 

8.40 

7020 

83.79 

19.15 

7810 

88.37 

9.84 

8600 

92.74 

20.49 

6240 

78.99 

8.41 

7030 

83.85 

19.16 

7820 

88.43 

9.85 

8610 

92.79 

20.50 

6250 

79.06 

8.42 

7040 

83.90 

19.17 

7830 

88.49 

9.86 

8620 

92.84 

20.50 

6260 

79.12 

8.43 

7050 

83.»o 

19.17 

7840 

88.54 

9.87 

8630 

92.90 

20.51 

6270 

79.18 

8.44 

7060 

84.02 

19.18 

7850 

88.60 

9.87 

8640 

92.95 

20,52 

6280 

79.25 

8.45 

7070 

84.08 

19.19 

7860 

88.66 

9.88 

8650 

93.01 

20.53 

6290 

7931 

8.46 

7080 

84.14 

19.20 

7870 

88.71 

9.89 

8660 

93.06 

20.54 

6300 

79.37 

8.47 

7090 

84.20 

19.21 

7880 

88.77 

9.90 

8670 

93.11 

20.54 

6310 

79.44 

8.48 

7100 

84.26 

19.22 

7890 

88.83 

9.91 

8680 

93.17 

20.55 

6320 

79.50 

8.49 

7110 

84.32 

19.23 

7900 

88.88 

9.92 

8690 

93.22 

20.56 

6330 

79.56 

8.50 

7120 

84.38 

19.24 

7910 

88.94 

9.92 

8700 

9:5.27 

20.57 

6340 

79.62 

8.51 

7130 

84.44 

19.25 

7920 

88.99 

9.93 

8710 

93.33 

20.57 

6350 

79.69 

8.52 

7140 

84.50 

19.26 

7930 

89.05 

9.94 

8  20 

93.38 

20.58 

6360 

79.75 

8.53 

7150 

84.56 

19.26 

7940 

89.11 

9.95 

8  30 

93.43 

20.59 

6370 

79.81 

8.54 

7160 

84.62 

19.27 

7950 

89.16 

9.96 

8  40 

93.49 

20.60 

6380 

79.87 

8.55 

7170 

84.68  !  19.28 

7960 

89.22 

9.97 

8  50 

93.54 

20.61 

6390 

79.94 

sise 

7180 

84.73  :  19.29 

7970 

89.27 

9.97 

8  60 

93.59 

20.61 

6400 

80.00 

8.57 

7190 

84.79   19.30 

7980 

89.33 

9.98 

8  70 

93.65 

20.6.2 

6410 

80.06 

8.58 

7200 

84.85 

19.31 

7990 

89.39 

9.99 

8  80 

93.70 

20.63 

6420 

80.12 

8.59 

7210 

84.91 

19.32 

8000 

89.44 

20.00 

8  90 

93.75 

'20.64 

6430 

80.19 

8.60 

7220 

84.97 

19.33 

8010 

89.50 

20.01 

8800 

93.81 

20.65 

6440 

80.25 

8.60 

7230 

85.03 

19.34 

8020 

89.55 

20.02 

8810 

93.86 

20.65 

6450 

80.31 

8.61 

7240 

85.09 

19.35 

8030 

89.61 

20.02 

8820 

93.91 

20.66 

6460 

80.37 

8.62 

7250 

85.15 

19.35 

8040 

89.67 

20.03 

8830 

93.  97 

20.t>7 

6470 

80.44 

8.63 

7260    85.21  !  19.36 

8050 

89.72 

20.04 

8840 

94.02 

20.68 

6480  !  80.50 

8.64 

7270    85.26  j  19.37 

8060 

89.78 

20.05 

8850 

94.07 

20.68 

6490    80.56 

8.65 

7280    85.32   19.38 

8070 

89.83 

20.06 

8860 

94.13 

20.  6» 

6500    80.62 

8.66 

7290    85.38 

19.39 

8080 

89.89 

20.07 

8870 

94.18 

20.70 

6510    80.68 

8.67 

7300 

85.44 

19.40 

8090 

89.94 

20.07 

8880 

94.23 

20.71 

6520    80.75 

8.68 

7310 

85.50 

19.41 

8100 

90.00 

20.08 

8890 

94.29 

20.72 

6530    80.81 

8.69 

7320    85.56 

19.42 

8110 

90.06 

20.09 

8900 

94.34 

20.72 

6540    80.87 

8.70 

7330    85.62 

19.43 

8120 

90.11 

20.  0 

8910 

94.39 

20.73 

6550    80.93 

18.71 

7340    85.67 

19.43 

8130 

90.17 

20.  1 

8920 

94.45 

20.74 

6560    80.99 

18.72 

7350 

85.73 

19.44 

8140    90.22 

20.  2 

8930 

94.50 

20.75 

6570    81.06 

18.73 

7360 

85.79 

19.45 

8150    90.28 

20.  2 

8940 

94.55 

20.75 

6580  ,  81.12 

18.74 

7370    85.85 

19.46 

8160    90.33   20.  3 

8950 

94.60 

20.76 

6590    81.18 

18.75 

7380    85.91 

19.47 

8170 

90.39   20.  4 

8960 

94.66 

20.71 

6606    81.24 

18.76 

7390    85.97 

19.48 

8180 

90.44   20.  5 

8970 

94.71 

20.78 

6610    81.30 

18.77 

7400    86.02 

19.49 

8190    90.50   20.  6 

8980 

94.76 

20.79 

6620    81.36 

18.78 

7410    86.08 

19.50 

8200    90.55  1  20.  7 

8990 

94.82 

20.79 

6630    81.42 

18.79 

7420    86.14 

19.50 

8210 

90.61  I  20.  7 

9000 

94.87 

20.  SO 

6640    HI.  49 

18.80 

7430    86.20 

19.51 

8220    90.66  j  20.  8 

9010 

94.92 

20.W 

6650 

81.  55 

18.81 

7440    86.26 

19.52 

8230    90.  T2  \  20.  9 

9020 

9».97 

20.82 

6660 

81.61 

18.81 

7450  !  86.31 

19.53 

8240    90.77  ;  20.  0 

9030   95.03 

20.82 

6670    81.67 

18.82 

7460  i  86.37 

19.54 

8250 

90.83   20.  1 

9040   95.08  i  20.83 

6680  ,  81.73 

18.83 

7470    Mi.  43 

19.55 

8260 

90.  MS   20.  1 

9050   95.13   20.84 

6690 

81.79 

1K.K4 

74X0    86  49 

1956 

8270 

90.94   20.  2 

9060   95.18   20.8& 

6700 

81.85 

18.80 

7490    86.54 

19.57 

6280 

90.99 

20.23 

9070   95.24  j  20.B& 

TABLE  NO.  72— CON.  1U7 

From  Trautwine's  "Civil  Kn^iiieer'N  Pocket   Book." 


SQUARE  AND  Cl'BE  ROOTS,      r 


Square  Roots  and  Cube  Roots  ol  > umbers  fi 

—  (CONTINUED.) 


Num. 

Sq.  Rt. 

Cu.  Rt. 

Xum.   Sq.  Rt.  Cu.  Rt. 

Num. 

Sq.  Rt.  Cu.  Rt. 

Num. 

Sq.  Rt.  <'u.  Rt. 

90H> 

95.29 

20.86 

9320 

96.54   21.04 

9550 

97.72    21.22 

97M) 

98.89    21.39 

9090 

95.34 

20.87 

9330 

96.59   2 

1  .0:1 

9560 

97.78  ,  21.22 

9790 

9M.94    21.39 

9100 

95.39 

20.88 

9340 

96.64 

l.Oti 

9.-.7U 

97.83 

21.23 

9800 

9K.99 

21.40 

9iio 

95.45 

20.  h9 

9350    96.70 

1.07 

9580 

;»7  >-* 

21.24 

9810 

99.115    21.41 

9120 

95.50 

20.89 

9360 

96.75 

1.07 

9590 

97.93 

21.25 

9»20 

99.10  I  21.41 

in  30 

95.55 

20.90 

9370 

W.sO 

l.i  is 

9600 

97.98   21.2;> 

9*30 

99.15   21.42 

9140 

96.60 

20.91 

9380 

9t;.>5 

.09 

9610 

9K03  '  21.26 

9840 

99.20 

21.43 

9150 

95.66 

20.92 

9390 

96.90 

.10 

9620 

98.08   21.27 

9850 

99.25    21.44 

9160 

95.71 

20.92 

9400 

96.95  | 

.10 

9630 

98.13   21.> 

9860 

99.30 

21.44 

9170 

95.76 

20.93 

9410 

97.01 

.11 

9640 

98  18  i  21.28 

9870 

99.35 

21.45 

«180 

95.81 

20.94 

9420 

97.06 

.It 

9650 

98.23  I  21.29 

9880 

99.40 

21.46 

MHO 

95.86 

20.95 

9430 

97.11 

.1.1 

9660 

96.29 

21.30 

9890 

99.45 

21.47 

.9200 

95.92   20.95 

9440 

97.16 

M 

9670 

9h.:-!4 

21.30 

9900 

99.50 

21.47 

9210 

95.97   20.96 

9450 

97.21 

.14 

9K*0 

98.39 

21.31 

9910 

99.55   21.48 

9220 

96.02 

20.97 

9460 

97.26 

.18 

9690 

98.44 

21.32 

9920 

99.60 

21.49 

9230 

96.07 

20.98 

9470 

97.  31    2 

.if, 

9700 

9h.49   21.33 

9930 

99.65    21.49 

9240 

96.12 

20.98 

9480 

9...  a   2 

.16 

9710 

9K54   21.33 

9940 

99.70 

21.50 

9250 

96.18 

20.99 

9490 

97.42   2 

.17 

9720 

98.59 

21.34 

9950 

99.75 

21.51 

9260 

96.23 

21.00 

9500 

97.47   2 

.IS 

9730 

98.64 

21.35 

9960 

99.80   21.52 

9270 

96.28 

21.01 

9510 

97.52   2 

.18 

9740 

98.69 

21.36 

9970 

99.85   21.52 

9280 

96.33 

21.01 

9520 

97.57   2 

.19 

9750 

9S.74   21.36 

9980 

99.90  i  21.53 

9290 

96.38 

21.02 

9530 

97.62   2 

.20 

9760 

98.79 

21.37 

9990 

99.95   21  .5i 

9300 

96.44 

21.03 

9540 

97.67  ;  2 

/.'I 

9770 

98.84 

21.38 

10006 

100.00 

21.54 

9310 

96.49 

21.04 

I 

To  liiid  Square    or  Cube  Roots  of  large  11  umbers  not  con- 
tained in  the  column  of  numbers  of  the  table. 

Such  roots  may  sometimes  be  taken  at  once  from  the  table,  by  merely  regarding  the  columns  of 
powers  as  being  columns  of  numbers;  and  those  of  numbers  as'being  those  of  roots.  Thus,  if  the 
sq  rt  of  25281  is  reqd,  first  fled  that  number  in  the  column  of  squares;  and  opposite  to  it,  in  the 
column  of  numbers,  is  its  sq  rt  159.  For  the  cube  rt  of  857375,  find  that  number  in  the  column  of 
cubes ;  and  opposite  to  it,  in  the  col  of  numbers,  is  its  cube  rt  95.  When  the  exact  number  is  not  con- 
tained in  the  column  of  squares,  or  cubes,  as  the  case  may  be,  we  may  use  instead  the  number  nearest 
to  it,  if  no  great  accuracy  is  reqd.  But  when  a  considerable  degree  of  accuracy  is  necessary,  the 
following  very  correct  methods  may  be  used. 

For  the  square  root. 

This  rule  applies  both  to  whole  numbers,  and  to  those  which  are  partly  (not  wholly)  decimal.  First, 
im  the  foregoing  manner,  take  out  the  tabular  number,  which  is  nearest  to  the  given  one ;  and  also  its 
tabular  sq  rt.  Mult  this  tabular  number  by  3  ;  to  the  prod  add  the  given  number.  Call  the  sum  A. 
Then  mult  the  given  number  by  3 ;  to  the  prod  add  the  tabular  number.  Call  the  sum  B.  Then 

A  :  B  :  :  Tabular  root  :  Reqd  root. 

Ex.  Let  the  given  pumber  be  946.53.  Here  we  find  the  nearest  tabular  number  to  be  947 ;  and  its 
tabular  sq  rt  30.7734.  Hence, 

947  =  tab  num  1  f  946.53  =:  given  num. 

3  3 


2841 
946.53  =  given  num. 


and 


-i  2839.59 

947     =  tab  num. 


Tab  root. 
J0.7734 


Reqd  root. 
30.7657  +. 


Then  3787*.53 

The  root  as  found  by  actual  mathematical  process  is  also  30.7657  -}-. 

For  the  cube  root. 

This  rule  applies  both  to  whole  numbers,  and  to  those  whJch  are  partly  decimal.  First  take  out  tTie 
tabular  number  which  is  nearest  to  the  given  one;  and  also  its  tabular  cube  rt.  Mult  this  tabular 
number  by  2 ;  and  to  the  prod  add  the  given  number.  Call  the  sum  A.  Then  mult  the  given  number 
by  2;  and  to  the  prod  add  the  tabular  number.  Call  the  sum  B.  Then 

A  :  B  :  :  Tabular  root  :  Reqd  root. 

Ex.  Let  the  given  number  be  7368.  Here  we  fi»d  thejjearest  tabular  number  (in  the  column  of 
tube*)  to  be  6859 ;  and  its  tabular  cube  rt  19.  Hence, 

6859  =  tab  num.       ^  r     73^  -  giv,n  DHm. 

!  I f 

13718  ',  and       \    14736 

7368  =  given  num.  6859  =  tab  num. 

21086- A.  [  21595 -B. 

A.  B.  Tab  Root.    Reqd  Rt. 

Then,  as  21086      :       21595      :  :       19      :       19.45*5 
The  root  as  found  by  correct  mathematical  process  is  19.4588.     The  engineer  rarelv  rpniiires  even 


198 
From  Trautwine's  ••  Civil  Engineer's  Pocket  Book. 


SQUARE  AND  CUBE  ROOTS. 

this  degree  of  accuracy  ;  for  his  purposes,  therefore,  this  process  is  greatly  preferable  to  the  ordinary 
laborious  one. 

To  find  the  square  root  of  a  number  which  is  wholly 
decimal. 

Very  simple,  and  correct  to  the  third  numeral  flgure  inclusive.  If  the  number  does  not  contain  at 
least  five  figures,  counting  from  the  first  numeral,  and  including  it,  add  one  or  more  ciphers  to  make 
five.  If,  after  that,  the  whole  numher  is  not  separable  into  twos,  add  another  cipher  to  make  it  so. 
Then  beginning  at  the  first  numeral  figure,  and  including  it,  assume  the  number  to  be  a  whole  one. 
In  the  table  find  the  number  nearest  to  this  assumed  one  ;  take  out  its  tabular  sq  rt  ;  move  the  deci- 
mal poiut  of  this  tabular  root  to  the  left,  half  as  many  places  as  the  finally  modified  decimal  number 
has  figures. 

Ex.  What  is  the  aq  rt  of  the  decimal  .002?  Here,  in  order  to  have  at  least  five  decimal  figures, 
counting  from  the  first  numeral  (2).  and  including  it,  add  ciphers  thus,  .00.20,00.0.  But,  as  it  is  not 
now  separable  into  twos,  add  another  cipher,  thus,  .00,20,00.00.  Then  beginning  at  the  first  numeral 
(t),  assume  this  decimal  to  be  the  whole  number  200000.  The  nearest  to  this  in  the  table  is  199809; 
and  the  sq  rt  of  this  is  447.  Now.  the  decimal  number  as  finally  modified,  namely,  .00.20,00,00,  has 
eight  figures  ;  one-half  of  which  is  4;  therefore,  move  the  decimal  point  of  the  root  447,  four  places  to 
the  left;  making  it  .0447.  This  is  the  reqd  sq  rt  of  .002,  correct  to  the  third  numeral  7  included. 

To  find  the  cube  root  of  a  number  which  is  wholly  decimal. 

Very  simple,  and  correct  to  the  third  numeral  inclusive. 

If  the  number  does  not  contain  at  least  five  figures,  counting  from  the  first  numeral,  and  including 
It,  add  one  or  more  ciphers  to  make  five.  If,  after  that,  the  number  is  not  separable  into  threes,  add 
one  or  more  ciphers  to  make  it  so.  Then  beginning  at  the  first  numeral,  and  including  it,  assume 
the  number  to  be  a  whole  one.  In  the  table  find  the  number  nearest  to  this  assumed  one,  and  take 
out  its  tabular  cub  rt.  Move  the  decimal  point  of  this  rt  to  the  left,  one-third  as  many  places  as  the 
finally  modified  decimal  number  has  figures. 

Ex.  What  is  the  cube  rt  of  the  decimal  .002?  Here,  in  order  to  have  at  least  five  figures,  counting 
from  the  first  numeral  (2),  and  including  it,  add  ciphers  thus,  .002,000,0.  But  as  it  is  not  now  separ- 
able into  threes,  add  two  more  ciphers  to  make  it  so  ;  thus,  .002,000,000.  Then  beginning  with  the 
first  numeral  (2),  assume  the  decimal  to  be  the  whole  number  2000000.  The  nearest  cube  to  this  in 
the  table  in  the  column  of  cubes,  is  2000376  ;  and  its  tabular  cube  rt  as  found  in  the  col  of  numbers, 
is  126.  Now,  the  decimal  number  as  finally  modified,  namely,  .002  000  000,  has  nine  figures  ;  one-third 
of  which  is  3;  therefore,  move  the  decimal  point  of  the  root  126,  three  places  to  the  left,  making  it 
.126.  Thia  is  the  reqd  cube  rt  of  the  decimal  .002,  correct  to  the  third  numeral  6  included. 


To  flnd  roots  by  logarithm* 

For  tables  of  sq.  rts.  of  5th  powers  see  table  69,  page  166. 

To  find  the  sq.  or  cu.  rt.  of  a  number  consisting  of  intigers 
and  decimals. 

Multiply  the  difference  between  the  root  of  the  intiger  part  of  the  given 
number,  and  the  root  of  the  next  higher  number,  by  the  decimal  part  of 
the  given  number,  and  add  the  product  to  the  root  of  the  given  intiger. 
The  sum  is  the  root  required. 

Ex.—  Required  the  sq.  rt.  of  20.321—  square  root  of  21  =  4.5825 

"     "  20  =  4.4721 
Difference  =    .1104 

.1104  X  .321  =  .354384,  add  to  rt.  of  20,  4.4721,  and  get  4.5075384=rt.  required. 
Ex.—  Required  the  cu.  rt.   of  16.42—  cube  root  of  17  =  2.5712 

"     "  16  =  2.5198 
Difference  =    .0514 
.0514  X  .42  =  .021588,  add  to  rt.  of  16,  2.5198,  and  get  2.541388  =  rt.  required. 

To  find  the  sq.  or  cu.  rt.  of  a  higher  number  than  is  contain- 
ed in  the  table,  when  the  number  is  divisib  e  by  4  or  8  with- 
out leaving  a  remainder. 

RULE.—  Divide  the  number  by  4  or  8  respectively,  as  the  sq.  or  cu.  rt.  is  re- 
quired ;  take  the  rt.  of  the  quotient  in  the   table,  multiply  it  by  2, 
and  the  product  will  be  the  root  required. 
Ex.—  What  are  the  square  and  cube  roots  of  2400? 

2400  -h  4  =  600  and  2400  -*-  8  =  300. 

Then  thesq.  rt.  of  600,  per  table,  =  24.4949,  which,  being  X  2  =  48.9898  = 
sq.  rt.  required. 

Then  the  cu.  rt.  of  300,  per  table,  =  6.6943,  which,  being  X  2  =  13.3886  = 
cu.  rt.  required. 

To  find  the  4th  root  of  any  number. 

Take  the  square  root  of  its  square  root. 

To  find  the  6th  root  of  any  number. 

Take  the  cube  root  of  its  square  root. 

To  flnd  any  root  or  any  power  by  logarithms  see  pages  200  and  202. 


TABLE  NO.  77. 
Logarithms  of  Numbers,  from  0  to  1OOO.* 


199 


Vo. 

O    1 

2 

3    4 

5 

6 

7 

8 

9 

Prop. 

0 

0 

00000 

30103 

4771260206 

6989" 

77815 

84510 

90309 

95424 

10 

00000 

00432 

00860 

0128301703 

02118 

02530 

02938 

03342 

03742 

415 

11 

04139 

04532 

04921 

05307  05690 

06069 

06445 

06818 

07188 

07554 

379 

12 

07918 

08278 

08636 

0899009342 

09691 

10037 

10380 

10721 

11059 

349 

13 

11394 

11727 

12057 

12385  12710 

13033 

13353 

13672  13987 

14301)  323 

14 

14613 

14921 

15228 

15533J15836 

16136 

1C435 

16731  1702f 

173181  300 

15 

17609 

17897 

18184 

18469 

18752 

19033 

19312 

19590  19s»if> 

20139)  281 

16 

20412 

20682 

20951 

21218 

21484 

21748 

2201U 

22271  22530 

22788 

264 

17 

23045 

23299 

•23552 

23804 

24054 

24303 

24551 

24797  25042 

25285 

249 

18 

25527 

25767  !  26007 

26245 

26481 

26717 

2(5951 

27184  27415 

27646 

236 

19 

27875 

28103  j  28330 

28555128780 

29003 

29225 

29446 

29666 

29885 

223 

80 

30103 

30319 

30535 

30749:30963 

31175 

31386 

31597 

31806 

32014 

212 

21 

32222 

32428 

32633 

32838  133041 

33243 

33445 

33646 

33845 

34044 

202 

22 

34242 

34439 

34635 

3483035024 

35218 

35410 

35602 

35793 

35983 

194 

23 

36173  36361 

36548 

3673536921 

37106 

37291 

37474 

37657 

37839 

185 

24 

38021  38201 

38381 

38560  38739 

38916 

39093 

39269 

39445 

39619 

177 

25 

39794  39967 

40140 

40312 

40483 

40654 

40824 

40993 

41162 

41330 

171 

26 

41497  41664}  41830 

41995 

42160 

42324 

42488 

42651 

42813 

42975 

164 

27 

43136!  43296 

43456 

43616  43775 

43933 

44090 

44248 

44404 

44560 

158 

28 

447161  44870 

45024 

45178  45331 

45484 

45636 

45788 

45939 

46089 

153 

29 

46240 

46389 

46538 

46686  46834 

46982 

47129 

47275 

47421 

47567 

148 

30 

47712 

47856 

48000 

48144 

48287 

48430 

48572 

48713 

48855 

48995 

143 

31 

49136 

49276 

49415 

49554 

49693 

49831 

49968 

50105 

50242 

50379 

138 

32 

50515  50650 

50785 

50920  51054 

51188 

51321 

51454 

51587 

51719 

134 

33 

51851 

51982  52113 

52244  j  52374 

52504 

52633 

52763 

52891 

53020 

130 

34 

53148 

53275  53402 

53529  53655 

53781 

53907 

54033 

54157 

54282 

126 

35 

54407  1  54530 

54654 

54777  54900 

55022 

55145 

55266 

55388 

55509 

122 

36 

556301  55750 

55870 

55990  56110 

56229 

56348 

56466 

56584 

56702 

119 

37 

56S20J  56937:  57054 

57170 

57287 

57403 

57518 

57634 

57749 

57863 

116 

38 

57978 

58092!  58206 

58319  58433 

58546 

58658 

58771 

58883 

58995 

113 

39 

59106 

592171  59328 

59439 

59549 

59659 

59769 

59879 

59988 

60097 

110 

40 

60206  1  603141  60422 

60530 

60638 

60745 

60852 

60959 

61066 

61172 

107 

41 

61278  1  61384  61489 

61595 

61700 

61804 

61909 

62013 

62118 

62221 

104 

42 

62325 

62428  62531 

6263462786 

62838 

62941 

63042 

63144 

63245 

102 

43 

63347 

63447  63548 

63648  63749 

63848 

63948 

64048  64147 

64246 

99 

44 

64345 

64443  64542 

64640  64738 

64836 

64933 

65030!  65127 

65224 

98 

45 

65321 

654171  65513 

65609  65705 

65801 

65896 

65991 

66086 

66181 

96 

46 

66276 

66370 

66464 

66558166651 

66745 

66838 

66931 

67024 

67117 

94 

47 

67210 

67302 

67394 

67486  67577 

67669 

67760 

67851 

67942 

68033 

92 

48 

68124 

68214 

68304 

6839468484 

68574 

68663 

68752 

68842 

68930 

90 

49 

69020 

69108 

69196 

69284  69372 

69460 

69548 

69635 

69722 

69810 

88 

50 

69897 

69983 

70070 

70156 

70243 

70329 

70415 

70500 

70586 

70671 

86 

51 

70757 

70842 

70927 

71011 

71096 

71180 

71265 

71349 

71433 

71516 

84 

52 

71600 

71683 

71767 

71850 

71933 

72015 

72098 

72181 

72263 

72345 

82 

53 

72428 

72509 

72591 

72672 

72754 

72835 

72916 

72997 

73078 

73158 

81 

54 

73239 

73319 

73399 

73480 

73559 

73639 

73719 

73798 

73878 

73957 

80 

55 

74036 

74115 

74193 

74272 

74351 

74429 

74507 

74585 

74663 

74741 

78 

56 

74818 

74896 

74973 

75050 

75127 

75204 

75281 

75358 

75434 

75511 

77 

67 

75587 

75663 

75739 

75815 

75891 

75966 

76042 

76117 

76192 

76267 

75 

68 

76342 

76417 

76492 

76566 

76641 

76715 

76789 

76863 

76937 

77011 

74 

59 

77085 

77158 

77232 

77305 

77378 

77451 

77524 

77597 

77670 

77742 

73 

60 

7T815 

77887 

77959 

78031 

78103 

78175 

78247 

78318 

78390 

78461 

72 

61 

78533 

78604 

78675 

78746 

78816 

78887 

78958 

79028 

79098 

79169 

71 

62 

79239 

79309 

79379 

79448 

79518 

79588 

79657 

79726 

79796 

79865 

70 

63 

79934 

80002 

80071 

80140 

80208 

80277 

80345 

80413 

80482 

80550 

69 

64 

80618 

80685 

80753 

80821 

80888 

80956 

81023 

81090 

81157 

81224 

68 

66 

81291 

81358 

81424 

81491 

81557 

81624 

81690  81766 

81822 

81888 

67 

*  Each  log  is  supposed  to  have  the  decimal  sign  before  it.  An  error  of 
less  than  1  in  the  final  decimal  exists  in  a  number  of  the  logs  of  this  table, 
it  will  not,  however,  be  material  in  ordinary  computations. 


2UO 


TABLE  NO.  78. 


Logarithms  of  Numbers,  from  O  to  1OOO*— (Continued.) 


No. 

0 

1 
1   |   2 

3 

4 

5 

6 

7 

9 

9 

Prop. 

66 

81954 

82020 

82085 

82151 

82216 

82282 

82347 

82412 

82477 

82542 

66 

67 

82607 

82672 

82736 

82801 

82866 

82930 

82994 

83058 

83123 

83187 

65 

68 

83250 

83314 

83378 

83442 

83505 

83569 

83632 

83695 

83758 

83821 

64 

69 

83884 

83947 

84010 

84073  84136 

84198 

84260 

84323 

84385 

84447 

63 

70 

84509 

84571 

84633 

84695  84757 

84818 

84880 

84941 

85003 

850f4 

62 

71 

85125 

85187  85248 

85309  85369 

85430 

85491 

85551 

85612 

85672 

61 

72 

85733 

85793  85853 

85913 

85973 

86033 

8«093 

86153 

86213 

86272 

60 

73 

86332 

86391  i  86451 

86510 

86569 

86628 

86687 

86746 

86805 

86864 

59 

74 

86923 

86981  87040 

87098 

87157 

87215 

87273 

87332 

87390 

87448 

58 

75 

87506 

87564'  87621 

87679 

87737 

87794  87852 

87909 

87966 

8S-024 

57 

76 

88081 

88138 

88195!  S8262 

88309 

88366  88422 

88479 

88536 

88592 

56 

77 

88649 

88705 

88761  88818 

88874 

88930!  88986 

89042 

89098 

89153 

56 

78 

89209 

89265 

89320 

89376 

89431 

894871  89542 

89597 

89652 

89707 

55 

79 

89762 

89817 

89872 

89927 

89982 

90036  90091 

90145 

90200  90254 

54 

80 

90309 

90363 

90417 

90471 

90525 

90579  90633 

90687 

90741 

90794 

54 

81 

90848 

90902 

90955 

91009 

91062 

91115 

91169  91222 

91275 

91328 

53 

82 

91381 

91434|  91487 

91540 

91592 

91645 

91698 

91750 

91803 

91855 

53 

83 

91907 

91960 

92012 

92064 

92116 

92168 

92220 

92272 

92324 

92376 

52 

84 

92427 

92479 

92531 

92582 

92634 

92685 

92737 

92788 

92839 

92890 

51 

85 

92941 

92993 

93044 

93095 

93146 

93196 

93247 

93298 

93348 

93399 

51 

86 

93449 

93500 

93550  93601 

93651 

93701 

93751 

93802 

93852 

93902 

50 

87 

93951 

94001 

94051!  94101 

94151 

94200 

94250 

94300 

94349 

94398 

49 

88 

94448 

94497!  94546  i  94596 

94645 

94694 

94743 

94792 

94841 

94890 

49 

89 

94939 

94987  !  95036  95085 

95133 

95182 

95230 

95279 

95327 

95376 

48 

90 

95424 

95472  95520;  95568 

95616 

95664 

95712 

95760 

95808 

95856 

48 

91 

95904 

95951  95999;  96047 

96094 

96142 

96189 

96236 

96284 

96331 

48 

92 

96378 

96426  96473:  96520 

96567 

96614 

96661 

96708 

96754 

96801 

47 

93 

96848 

96895  96941;  96988 

97034 

97081 

97127 

97174 

97220 

97266 

47 

94 

97312 

97359  i  97405  97451 

97497 

97543 

97589 

97635 

97680 

97726 

46 

95 

97772 

97818  97863  97909 

97954 

98000 

98045 

98091 

98136 

981  81'  46 

96 

98227 

98272 

98317 

98362 

98407 

98452 

98497 

98542 

98587 

98632 

45 

97 

98677 

98721 

98766 

98811 

98855 

98900 

98945 

98989 

99033 

99078 

45 

98 

99122 

99166  99211 

99255 

99299 

99343 

99387 

99431 

99475 

99519 

44 

99 

99563 

99607 

99651 

99694 

99738 

99782 

99825 

998691  999131  99956 

44 

*  See  foot  note  on  paere  199. 


The  log  of  2870  is  3.45788    I     The  log  of    .287  is  —  1.45788 
«      «     «     287  is  2.45788  "      "     "     .028  is  —  2.44716 

.002  is  —  3.30103 


287  is  2.45788 
28.7  is  1.45788 


2.87  is  0.45788 


.0002  is  —  4.30103 


What  is  the  log  of  2873? 
Here,  log  of  2870  =  3.45788 
And  prop  153  X  3  =          459 

3.458339 

To  find  roots  divide  the  log  (with  its  index)  of  the  given  number,  by  that 
•amber  which  expresses  the  kind  of  root.    The  quotient  will  be  the  log  of  the  required  root. 

Example.    What  is  the  cube  root  of  2870  ? 
Here,  the  log  of  2870,  with  its  index,  is  3.*5788.     And  --  -  -  =  1.15263.    Hence  the  cube  root  ia  14.2. 

The  Hyperbolic,  or  Napierian  logarithm  is  the  common  log  of 

the  table  multiplied  by  2.3025651. 

Sq.  rt.  6925=Log  3.84042-*-2=log  1.92021,  corresponding  No. =83. 2138= sq.  rt« 
Cu-rt.6925=  "     3.84042-*-3=  "    1.28014,  "  =19.0669=cu.  rt. 

4th  rt.  6925=  "     3.84042+4=  l<      '96010,  "  =  9.1222 = 4th  rt. 

Proceed  in  like  manner  for  any  other  root  required.    This  method  of  ex- 
tracting roots  is  more  rapid  and  simple  than  any  other. 


201 
EXPLANATION  AS  TO  TABLES  OF  LOGARITHMS. 

LO  G  A  R I T  H  M  S  are  the  exponents  with  which  a  fixed  number  must  be 
affected  in  order  to  produce  a  given  number.    The  fixed  number  is  called 
the  BASE.    The  base  of  the  common  system  of  logarithms  is  10. 
Since  10°  =     1  the  logarithm  of     1  is  0. 
"      101  =    10    "  "    10  "  1. 

"      102  -  100    "  "  100  "  2. 

Thus,  the  logarithms  of  all  powers  of  the  base  are  integral  numbers, 
while  the  logarithms  of  numbers  intervening  between  exact  powers  of  the 
base  are  composed  of  an  intiger  and  a  fractional  or  decimal  part — called 
the  MANTISSA.  The  integral  part  of  the  logarithm  being  called  the 

liunrxor  CHARACTERISTIC 

NOTE  WELL  THE  FOLLOWING   RULES. 

I.    The  log.  of  any  exact  power  of  10  is  a  positive  (+)  intiger 
one  less  than  the  number  of  places  in  the  number. 

Thus— See  figures  at  foot  of  table  on  page  200— 
Log  of  2870  has  3  for  its  index,  there  being  4  figures  in  the  number. 


2S7 

28 
2 


II.  The  characteristic  of  any  decimal  number  is  negative 
(—  )  and  numerically  one  more  than  the  number  of  zeros 
immediately  following  the  decimal  point. 

Thus  —  See  figures  on  page  200  (2d  column.) 

Log  of.  decimal  .287  (being  no  zeros)  =  —  1.  (  Negative,  and  1  in  excess  of 
.023  (    '          1  zero  )  =  —  2.  •<  the  number  of  zeros  immedi- 


.002  (    '          2  zeros]  =  —  3.  (  ately  following  deci'al  point. 
j     The  minus  sign^instead  of  being  placed  befori  the  index,   as     ) 
<     here  shown,  is  usually  placed  above  thei  ndex,  thus,    3. 

USE  OF  TABLE.  The  logarithms  of  numbers  from  1  to  9  are  taken 
from  the  top  horizontal  line  of  the  table,  Log  of  9  being  .95424  ;  and  logs  of 
numbers  from  1L  to  99  are  taken  from  the  first  column,  headed  by  O,  the 
index  1  being  added  as  above  explained  [IJ.  Thus—  the  log  of  91  =  1.95904, 
Log  of  80  =  1.90309.  Logs  of  numbers  from  100  to  1000  are  taken  from  the 
table  as  follows  —  required  the  log  of  915  ;  find  91  in  first  column  and  then 
run  horizontally  across  the  table  to  the  column  headed  5  where  is  found 
the  log  .96142  to  which  add  an  index  of  2,  as  above  explained,  making 
2.96142  the  log  required.  Log  of  800  would  in  like  manner  be  2.90309,  log 
of  801  =  2.90363.  Since  the  decimal  part  of  the  logarithm  is  not  changed  by 
multiplying  or  dividing  the  number  by  any  power  of  10  the  logarithm  of  a 
number  of  4  or  5  places  may  also  be  taken  from  the  table  as  shown  at  the 
foot  of  the  table.  The  log  of  287  =  2.45788  and  log  of  2870  =  3.45788—  the 
index  only  being  changed.  If,  however,  the  4th  figure  is  other  than  O,  as 
2873,  then  proceed  as  follows  :  —  find  the  log  of  the  3  left  hand  figures  and  in 
the  same  horizontal  line,  at  its  intersection  with  the  last  vertical  column, 
headed  •*  Prop."  [Proportionate  parts]  take  the  number  indicated  and 
multiply  it  by  the  last  figure  of  the  given  number  .  Exclude  one  figure 
from  the  product  and  add  the  remainder  to  the  log  first  found.  In  case 
as  shown  at  foot  of  table  log  is  taken  for  2870  then  in  last  column  is  found 
153  which  X  3,  the  last  number  of  the  given  number  2873,  exclude  the  right 
hand  figure  from  the  product  of  459  and  add  the  remainder,  45,  to  the  log 
first  found. 


What  is  the  log  of  28735? 
Here  log  of  28700  =  4.45788 
And  prop  153X35  =  53.55 

Log  of  28735  =4.45841 


Here  2  figures  are  cast  off  because  there 
are  2  figures  in  the  multiplier  [35] .  With 
numbers  of  5  figures  this  may  be  in  error 
1  in  the  last  decimal. 


202 

In  the  use  of  logarithms  it  is  not  only  necessary  to  find  the  log  corres- 
ponding to  a  given  number  but  also  to  find  the  number  corresponding  to 
any  given  log. 

III.    Given  any  log  to  find  the  corresponding  number. 

A.  —  Where  the  mantissa  is  found  in  the  table. 

Look  in  the  table  for  the  given  log,  take  out  the  corresponding  number 
and  place  the  decimal  point  according  to  the  given  index. 

Example— Given  log  4.96142,  what  is  the  corresponding  number? 

Look  in  table  for  log  96142  and  find  it  corresponds  to  the  number  915. 
The  given  index  4  indicates  a  number  of  5  places  therefore  point  off  the 
number  obtained  to  have  5  places  and  to  read  91500. 

Log  of  2.90309  corresponds  to  800;  Log  .30103  to  2.  &c. 

B. — Where  the  mantissa  is  not  found  in  the  table. 

Take  from  the  table  the  next  lesser  mantissa  and  its  corresponding  num- 
ber. Then  subtract  this  mantissa  from  the  given  one  and  divide  the  re- 
mainder by  the  number  opposite  in  the  column  "  Prop."  Annex  the  quo- 
tient so  found  to  the  tabular  number  taken  out  and  then  point  off  as  indi- 
cated by  the  given  index. 

Example— Given  the  log  1.96166  to  find  the  corresponding  number . 

From  table  we  find  .96142  to  be  the  nearest  lesser  mantissa  and  915  to  be 
the  corresponding  number.  .96166,  the  given  mantissa,  minus  .96142  the 
lesser  one  =  difference  of  24  which  being  divided  by  48,  the  number  found 
in  column  "  Prop."  =  .5.  This  being  annexed  to  the  tabular  number  915= 
9155.  The  given  index  1  indicates  a  number  of  2  places,  so  91.55  becomes 
the  required  number, 

THE  USE  OFLOGARITHMS. 


The  ADDITION  of  logarithms  corresponds  to  ordinary  MULTIPLICA- 
TION and  any  number  of  given  numbers  either  integral,  decimal  or  mixed, 
may  be  multiplied  togeth 

Thus :  multiply  togethe 
Log  166.        =        2.22010 


may  be  multiplied  together  by  one  operation 
Thus :  multiply  together  166,  71.5,  8.25  and  .078  (=7637.7). 


71.5   =   1.85430 
8.25  =   0.91645 
.078  =  —2. 


Note.  The  index  of  the  last  log  being 
minus  it  is  subtracted  from  the  sum  of  the 
-f-  indices,  5,  leaving  3  the  index  of  the  sum. 

"  of  product  =  3.8 

By  method  B,  above  given,  the  log  3.88294  is  found  to  correspond  to  the 
number 7637. 7  which  is  the  required  product. 

The  SUBTRACTION  of  logarithms  corresponds  to  ordinary  DIVISION. 
The  log  of  the  divisor  being  subtracted  from  the  log  of  the  dividend  gives, 
as  a  remainder,  the  log  of  the  quotient. 

Thus— Divide  86.32  by  6.85  (=12.601) . 
Log  86. 32      =    1.93611 

"     6.85       =    0.8 


"  quotient=    1.10042,  which,  by  method  "  B,"  =  12.601  =  quotient. 

TO   RAISE  A  NUMBER  TO  A  POWER. 

Rule.— Multiply  the  log  of  the  number  by  the  exponent  of  the  power  and 
find  the  number  corresponding  to  the  product. 

Thus— What  is  the  5th  power  of  7.65? 

Log  of  7.65=  .88366  which  X  5  =  4.41830  the  number  corresponding  to 
which  is  26200. 

TO   FIND  ANY  ROOT  BY  LOGARITHMS. 

See  explanation  at  foot  of  table  on  page  200.  The  cube  root  14.2  being 
the  number  corresponding  to  log  1.15263.  Proceed  in  like  manner  for  any 
other  root  required . 


203 

The  foregoing  explanations  as  to  the  use  of  logarithms  are  cheifly  for 
the  benefit  of  those  who  have,  by  disuse,  become  '"rusty"  in  the  use  of  the 
tables ;  although  any  one  may  in  a  day  or  two  become  f amilliar  with 
them  and  may,  by  their  use,  greatly  lessen  the  drudgery  of  mathematical 
calculations.  Such  uses  only  have  been  explained  as  pertain  to  the  sim- 
pler mathematical  operations. 


EXPLANATION   OF   CHARACTERS. 

The  following  brief  explanation  is  given  of  a  few  of  the  more  com- 
mon characters  used  in  calculations,  etc.  and  which  are  so  frequently 
met  with  in  mathematical  and  similar  works. 

=    Signifies    Equality,  as  2  +  2  =  4. 

-f-  "  Plus,  as  2  +  2  =  4. 

"  Multiplied  by,      as  2  X  4  =  8. 

"  Minus,  as  8  —  2  =  6. 

-f-  Divided  by,  as  8  -*-  2  =  4. 

:  & : :     "  Proportion,          as  2  : 8  : :  4  : 16        reads ....  as  2  is  to  8 

so  is  4  to  16,    or,  2  is  to  8  as  4  is  to  16. 
The  Vinculum  or  Bar  indicates  that  all  the  numbers 
over   which  it  is  placed    are  to  be   considered  as  one 
quantity,  thus,  2  •-(-  8  -*-  2  =  5 ;  or  5X8—  2  =30. 

(    )     [    ]          Parenthesis  or  Brackets       indicate,  as  in  above,   that 
all  included  figures  are  to  be  considered  as  one  quan- 
tity, thus,  (  3  X  5  )  -f 10  =  25 ;  or  3  X  [  5  +  10  ]  =  45. 
Decimal  Point. 

V  The  Radical  or  Root  sign    when  placed  before  a  num 

ber  indicates  that  the  square  root  of  the  number  is 
required,  \  16  =  4;  \15  -f- 10  =  5.  The  degree  of  the 

root,  other  than  the  square  root,  is  indicated  by  a 
figure  placed  above  the  radical,  which  figure  is 
called  the  Index.  V  =  Cube  root ;  *y  =  4th.  root  etc. 

Z     Signifies    Angle. 

J.  "          Perpendicular. 

A  Triangle,  or  triangular          as  A  iron  or  inches. 

Square,  as    n     "      "       " 

O  Circle  or  Circular,  as  O     '*      "        ** 

Therefore    or    Hence. 
"  Because. 

ft  The  Ratio  of  the  circumference  of  a  circle  to  its  diam- 

eter,   which  =  3.1416  . 
>   <  Greater  and  Less,  a>  b  reads  -  a  greater  than  b. 

00  Infinity. 

Degrees.  Minutes,  and  Seconds  of  arc. 
"  Feet  and  Inches. 

1  I  &c.    •'  when  set  superior  to  a  number,   that  the  square  or  cube 

root  etc.  is  wanted,  thus  25$  indicates  the  sq.  rt.of  25. 
i  f  I  <fec.  "         when  set  superior  to  a  number,  respectively,  the  sq.  rt. 

of  the  cube;  the  sq.  rt.  of  the  5th.  power;  and  the  cube 

root  of  the  6th.  power  etc. 
236  &c.  "        when  set  superior  to  a  number,  the  power  to  which  the 

number  is  to  be  raised,    thus  2s  =  4 ;  23  =  8 ;  25  =  32  &c. 


204 


CONCLUSION. 

The  public  may  claim  that  the  author  owes  to  them  an  apology  for  hav- 
ing presented  an  irrigation  manual  wherein  no  direction  is  given  as  to  the 
detail  workings  of  an  irrigation  plant,  or  any  direction  as  to  wrhen,  and 
how  often,  to  irrigate,  how  to  prepare  the  soil,  &c.  Such  was  not  the  ob- 
ject, as  stated  in  the  preface,  but  rather  to  present  certain  items  of  techni- 
cal information,  and  such  other  matter  as  would  tend  to  show  the  import- 
ance and  practicability  of  irrigation  in  the  Dakotas.  The  subject  is  one 
too  vast  to  be  treated  fully  in  one  volume,  or  in  a  score  of  volumes,  such  as 
this.  More  has  been  omitted  than  has  been  included,  and  much  which 
was  of  value,  and  which  it  was  desired  to  include,  has  been  omitted  be- 
cause of  the  limited  means  and  space,  and  the  circumstances  under  which 
this  little  book  was  made.  Should  it  become  advisable  to  issue  a  second 
edition  many  additional  features  of  interest  and  of  value  will  be  included. 
A  start  has,  however,  been  made  which  it  is  to  be  hoped  others  will  more 
successfully  emulate  until  all  of  the  people  of  these  states  shall  have  be- 
come imbued  with  the  vital  importance  to  themselves  and  to  their  child- 
ren of-  this  matter  of  irrigation ;  and  until  the  thousands  of  acres  of  our 
now  waste  paradise  shall  have  put  on  that  cloak  of  perrennial  verdure 
which  is  their  due  and  their  destiny. 

No  more  fitting  conclusion  can  be  made  than  to  quote  from  the  eloquent 
words  of  the  late  Hon.  S.  S.  Cox,  congressman  from  New  York,  delivered 
in  his  oration  at  Huron  on  July  4th,  1889.  Words  as  poetic  in  sentiment 
as  they  are  prophetic  of  truth.  He  said : 

'•  But  yesterday  your  fruitful  valley  was  whitened 
with  the  bones  of  the  buffalo.  Now  it  is  an  ideal 
farming  area.  It  is  a  lesser  Nile  region,  without  its 
overflow.  Artesian  Wells  give  water  where  the  sun 
once  made  drouth  perrennial.  The  water  power  of 
your  matchless  valley  is  as  yet  immeasurable  by 
ordinary  mechanical  standards.  It  is  so  prevalent 
that  your  people  will  utilize  its  specific  gravity  for 
the  diversity  of  their  industries.  When  its  undi- 
minished  flow  and  steady  pressure  from  the  bosom 
of  the  earth  are  properly  harnessed  by  mechanism, 
it  will  give  its  lucid  lymph  to  make  grasses  for 
stock  and  lawns  for  beautiful  homes.  Its  sunless 
currents,  through  the  ingenuity  of  man,  will  en- 
hance the  rich  soil  by  quenching  its  thirst.  Fab- 
ulous are  the  wasted  energies  of  your  water  power, 
as  we  count  it  by  the  standard  horse  power  of  me- 
chanics; but  still  more  marvellous  are  the  real 
energies  of  the  soil  which  it  would  fructify. 

The  beautiful  and  fruitful  valley  of  the  James 
may  not  be  as  redolent  of  historic  association  and 
traditions  as  another  James  River  of  the  colonial 
days ;  but  deeper  than  historical  or  traditional  in- 
cident are  Dakota's  pure  springs  under  a  magic 
more  enchanting  than  that  of  Aladdin,  which  leap 
from  your  modern  Artesium. 


THE  END. 


Advertising  Appendix. 


THE  author,  on  behalf  of  the  public  for  whom  this  Manual  is  in- 
tended and  to  whom  it  will  come,  acknowledges  the  obligation  due  to 
the  advertisers  herein;  for  from  the  proceeds  of  this  feature  of  the 
book  has,  in  chief,  been  derived  the  funds  for  its  publication.  Had 
.it  not  been  for  this  patronage  the  book  could  not  have  been  made.  It 
is  hoped  and  expected  that  in  no  sense  has  this  been  a  charity,  but 
rather  a  good  paying  investment,  for  the  goods  advertised^will  be 
used  in  large  quantities  in  these  states  and  the  advertisers  deserve 
the  patronage  of  our  people  not  only  because  the  largest  and  most 
responsible  representatives  in  their  respective  lines,  but  because  of 
the^acknowledged  excellence  and  reputation  of  the  goods  they  rep- 
resent. 

The  informationjcontained  in  this  appendix  will  be  of  value  to  ir- 
rigators  and  others  who  often  find  difficulty  in  learning  as  to  where 
to  find  reputable  dealers  with  whom  to  deal.  Such  only  have  been 
solicited,  and  to  such  as  are  here  represented  our  people  fairly  owe 
their  patronage. 


206 


James  B.  Glow  Sf  Son, 

LAKE   AND   FRANKLIN   STREETS, 


Manufacturers  of  and  Dealers  in 


Wrought  Iron  Pipe, 
\  Artesian  Well  Tubing, 

-4 

Well  Casing^ 

Line  Pipe, 

Boiler  Tubes, 

Well  Tools, 

Fittings  &  Brass  Goods 

ALSO 

§cipplies  for  Clambers, 
@as  and  Steam  ^Titters  and 
Water 


SEND  FOR  CATALOGUE  AND  PRICES. 


207 


WELL  DRILLING  MBGHIflERY, 


MANUFACTURED  BY 


Willianjs  Brothers, 

ITHACA,  N.  Y. 


A.WUSCORO.MFD.OT. 


Mounted  and  on  Sills, 

FOR 

Deep  or  shallow  wells, 


WITH 


Steam  or  horse  power.- 

SEND  FOR  CATALOGUE. 


Address 


ITHACA,  N.  Y. 


208 


Engineering  News 


AMERICAN  RAILWAY  JOURNAL. 


Is  published  EVERY  THURSDAY  at  the  Tribune  Building,  NEW  YORK 
City.  It  is  a  60  page  paper,  was  established  in  1874,  and  it  is  the 
PIONEER  in  publishing  the  news  of  ENGINEERING  CONSTRUCTION 
WORK  throughout  the  Continent.  It  was  the  first  journal  in  Ameri- 
ca to  make  a  specialty  of  WATER  WORKS  construction  and  it 
still  maintains  its  lead  in  that  large  and  growing  interest  over  all  its 
competitors. 

ENGINEERING  NEWS  was  the  first  American  journal  which  paid 
particular  attention  to  the  subject  of  IRRIGATION,  and  it  has 
published  more  valuable  information  on  this  important  interest  of  the 
arid  regions  of  the  west  than  all  other  American  papers  combined. 
It  was  the  only  Engineering  journal  in  America  specially  represented 
at  the  IRRIGATION  CONGRESS  recently  held  in  Salt  Lake  City,  and 
it  is  now  the  only  paper  East  of  Denver  which  is  interested  in  the 
great  question  of  Irrigation. 

ENGINEERING  NEWS  is  a  national  journal;  it  circulates  in  every 
state  and  territory  on  the  American  Continents — from  Alaska  to  the 
Argentine  Republic;  it  is  read  by  more  contractors  and  hydraulic 
engineers  than  all  other  engineering  newspapers  combined  and  is  an 
especially  favorable  medium  for  advertising  PROPOSALS  FOR 
IRRIGATION  WORKS  to  be  constructed  in  the  West. 

The  price  of  the  paper  is  $5.00  per  year;  the  cost  of  advertising 
proposals  for  contracts  is  20  cents  per  line  of  seven  words  to  the  line. 

If  you  want  to  get  the  services  of  the  best  contractors  for  the  low- 
est price  try  an  advertisement  in  ENGINEERING  NEWS. 


ADDRESS 

ENGINEERING    NEWS    PUBLISHING  CO., 

TRIBUNE    BUILDING,    NEW    YORK. 


209 


H  Great  Work  or?  Irrigation, 

A  magnificent  double  volume  containing 
over  800  pages  devoted  to  irrigation  progress  in 
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in  Irrigation  Canals  "  is  now  ready  for  distribu- 
tion. It  is  written  by  P.  J.  Flynn,  the  famous 
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have  this  book.  Price  for  both  volumes  $8.00. 
Send  your  order  to 

Irrigation  Rjge, 

gait  CaHe  &!#,  U«ab. 


THE  IRRIGATION  AGE. 

(EhE  Pioneer  Irrigation  Journal  o!  ttys  World. 

PUBLISHED  SEMI-MONTHLY  BY  THE 

Bmyttye,  Britten  &  POOFE  Go. 

Offices: 

Salt  Lake  City.  San  Francisco. 

Denver.  Washington. 


Invaluable  to  every  farmer  of  Qal^ota. 


SUBSCRIPTION  PRICE,  $2.00  PER  YEAR. 


210 


CHAPMAN  l/ALlfE  MANFG.  BO, 


Works  and  General  Office, 
Indian  Orchard,  Mass. 
JASON  GILES,  Gen,  Mgr. 


Treasurer's  Office, 
72  KilbySt.,  Boston,  Mass, 
C.  J.  GOODWIN,  Treasurer, 


Chicago  Office,  24  W.  Lake  St,      E.  W.  BUSS,  Western  Mgr. 


GATE  VALVES 

for  steam  or  water.    Also 

FiFE 

THE  CHAPMAN  VALVES  ARE  THE  BEST 
AND  MOST  DURABLE  MADE. 


A  full  stock  always  on  hand  in  Chicago. 
Give  us  a  trial.  • 


211 

THE  CHICAGO 

*  WATER  MOTOR  * 

For  running  by  Artesian  Wells  or  Hydrant  Pressure,  Sewing  Ma- 
chines, Dental  Lathes,  and  Engines,  Organs,  Printing  Presses,  Saus- 
age Machines,  Coffee  Mills,  Corn  and  Feed  Mills,  Ventilating  Fans, 
Ice  Cream  Freezers,  Elevators,  Electric  Lights,  &c. 

We  have  more  motors  in  use  IN  DAKOTA,  than  all  other  makes 
combined. 

"Huronite,"  HURON,  S.  D.,  May  8,  1890. 
GENTS: 

Your  Double  Motor  we  regard  as  an  improvement  over  the  Tuerk. 
Signed:        SHANNON  &  LONGSTAFF. 

(The  above  after  using  a  Tuerk  Motor  2  years  purchased  one  of 
ours.) 

WATERTOWN,  S.  D.,  May  ist,  1890. 
GENTS: 

We  are  using  one  of  your  No.  1  1  Double  Motors  for  driving  Pony, 
cylinder  and  job  press  —  pressure  60  Ibs.  Our  former  superintendent 
put  a  Little  Giant  motor  in  our  office  but  we  found  that  this  motor, 
when  running  only  one  press,  used  more  water  than  yours  when  run- 
ning two  presses;  and,  even  with  the  larger  consumption  of  water 
was  not  able  to  run  both  presses. 

Signed:        CONKLIN  &  REDDICK, 

Publishers,  Conklin's  Dakotian. 

WE  WILL  MAKE 


THAN  ANY   OTHER 


first  Glass 


CAN  ALSO  SELL  YOU  A 

WIND  MILL 

and  the  best  GRINDING  MILL  in  the  market. 

Address 

Chicago  Water  RBotor  Company, 

101  LAKE  ST.,  CHICAGO. 


212 


ST.  LOUIS 

WELL  ^irE  CO,, 


ST.  LOTJIS,  IMIO. 


MANUFACTURERS  OF 


WELL  MACHINERY, 

WELL  TOOLS, 
WELL  SUPPLIES. 


Address, 

St.  Louis  Well  Machine  &  Tool  Go, 

Wabash  Track  and  Newstead  Ave.  (South  44th  St.,; 
ST.  LOUIS,  MO. 


213 


We  find  it  to  oiJr  interest  to  lulu 

WROUGHT  IRON  PIPE 


for  steam  gas  and  water,  also 


T:\3Bma, 


PIPS, 

DRW  a  PIP^, 
Boiler  T  \ibes, 


FROM 


G.  W.  CRANE 
CO., 


'J 

Wholegale 

MINNEAPOLIS.  MINN. 


We  also  carry 


The  Most  Complete  Stock 


OF 


GOODS! 


in  the  Northwest. 


Send  for  Illustrated  Catalogue. 


214 

Bife's  Hydraulic  Engine 
(or  Ram ) 

Patented  February  8,  1887. 

For  supplying  water  to  Small  Towns,  Factories,  Steam  Mills,  Daries, 
Stock  Yards,  Railway  Tanks,  Residences,  and  for 


View  of  ram. 
Send  for  Catalogue. 


Constructed  on  new  and  improved  principles,  greatly  increasing 
the  capacity  and  avoiding  extreme  concussion  that  has-  heretofore 
proved  destructive  to  all  common  Hydraulic  Rams,  making  this 

Especially  Adapted 
to  Railroad  Water  Supply  and  Irrigation . 

The  following  is  an  extract  from  a  letter  to  the  company  from  a 
gentleman  who  is  using  one  of  these  rams  to  water  over  12  acres  of 
trees: 

OROVILLE,  CALIFORNIA,  Dec.  10,  1890. 

The  machine  is  doing  better  work  now  than  ever  before,  discharg- 
ing about  25  gallons  per  minute  or  the  enormous  amount  of  36,000 
gallons  per  day.  Signed:  D.  B.  HAYS. 

Write  for  illustrated  catalogue,  to 

Rife's  Bsfdraulic  gngine  Wg-  G°-» 
ROANOKE,  VIRGINIA. 

(•See  page  124  of  this  book.) 


215 

BUFF  &  BERBER, 

IMPROVED 


and  Surveying  Instruments, 


N*>.  9  Province  Court,  Boston,  Mass. 

They  aim  to  secure  in  their  Instuments.  —  Accuracy  of  division; 
Simplicity  in  manipulation;  Lightness  combined  with  strength;  Achro- 
matic telescope,  with  high  power;  Steadiness  of  adjustments  under  vary- 
ing temperatures;  Stiffness  to  avoid  any  tremor,  even  in  a  strong  wind, 
and  thorough  workmanship  in  every  part. 

Their  instruments  are  in  general  use  by  the  U.  S.  Government 
Engineers,  Geologists  and  surveyors,  and  the  range  of  instruments, 
as  made  by  them  for  River,  Harbor,  City,  Bridge,  Tunnel,  Railroad 
and  Mining  Engineering,  as  well  as  those  made  for  Triangulation  or 
Topographical  Work  and  Land  Surveying^  is  larger  than  that  of  any 
other  firm  in  the  country. 

Ilhistrated  Manual  and  Catalogue  sent  on  application. 


TRAUTWINE'S 

Civil  Engineer's  Pocket   Book. 

"If  you  can  own  but  a  single  book  let  it  be  this,  and  by  all  means 
have  this  if  you  are  but  a  rodman,  if  you  intend  to  continue  in  the 
work." — Railway  Age,  Oct.  9,  1884. 

"Without  doubt  it  has  proved  itself  to  be  the  most  useful  hand- 
book in  the  language  for  the  Engineering  profession." — Engineering 
and  Mining  Journal,  ,Aug  25,  1 888. 

"The  best  general  text-book  on  civil  engineering  in  the  English 
language.  It  is  a  whole  library  in  itself." — Engineering  News,  Jan. 
27th,  1883. 

"It  is  a  book  for  the  civil,  mechanical,  hydraulic  and  mining  en- 
gineer, and  architect  and  builder.  Its  tables  are  invaluable,  and  al- 
most absolute  reliance  can  be  placed  in  them." — Engineering  and 
Building  Record,  Aug.  nth,  1888. 

"It  is,  deservedly,  one  of  the  most  popular  of  Pocket  Books,  be- 
cause the  information  it  contains  is  presented  in  such  plain  terms  as 
to  be  readily  comprehended  by  those  who  have  not  had  the  advant- 
ages of  a  technical  education.  Every  statement  is  in  the  fewest 
words  that  will  clearly  convey  the  meaning." — American  Machinist, 
May  9th,  1885. 

For  sale  by  John  Wiley  <fc  Sons,  53  East  10th  St.,  New  York  City, 
or  by  J,  C,  Trautwine,  Jr.,  3301  Haverford  St.,  Philadelphia,  Pa, 

PRICE,  $500. 


216 


THEE 


flddpton  Pipe  X  Steel  Go,, 

CINCINNATI,  0. 

MAT 


FOR 


(^diverts, 
§ewers 

—  Irrigation. 


WATER   PIPE, 
GAS  PIPE. 


o!  Svery  BegcFiption. 

WRITE  US  FOR  ESTIMATES. 


217 


218 


P.  G,  HUSYIN  fllFG.  GO., 


MANUFACTURERS   OF 


ARTESIAN 

WELL  DRILLING 

MA  CHINER  Y. 


Pole  Tool  Rigs. 
Cable  Rigs. 
Hydraulic  Rigs. 
Jetting  Rigs. 
Turning  Rigs 

AND 

Combined  Rigs. 

ALSO 

Drilling  Tools 
and  Supplies. 


F,  G.  flUSTIN  MANFG,  GO,, 

CARPENTER    ST.    4    CARROLL    AVE. 

CHICAGO,  ILLINOIS. 

(Seepages  117  ,  n8&  next  page.) 


New  Era  Grader  and  Ditcher 

New  Era  Grader,  Ditcher  and  Wagon  Loader,  for  building 
irrigation  canals  and  storage  reservoirs  is  guaranteed  capable  of  plac- 
ing in  the  embankment  1000  to  1500  cubic  yards  of  earth  in  10  hours, 
with  6  teams  and  3  men,  at  a  cost  not  exceeding  2  cents  per  yard;  and 
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The  Best  Machine  for  building 

DITCHES,_ 


Austin  Steel  Reversible  Road  Machine. 

Austin's  Steel  Reversible  Road  3Iachine,  for  making  lateral  ditches 
and  building  country  roads,  will  build  J4  mile  of  lateral  ditch  per  day.  We 
also  make  Dump  Wagons :  Wheel,  Drag  and  Buck  Scrapers  and  Contract- 
or's Plows.  Send  for  catalogue  to  the 

F.  C.  Austin  Manfg.  Co.,  Chicago,  111.  CoTc°a™TAevneer  st> 


2250 

W.  &  L.    E.GURLEY, 

TIEtOY,  1ST.  IT. 

Largest  manufacturers  in  America  of  Civil  Engineers'  and   Sur- 
veyors' Instruments;  our  latest  illustrated  price  list  on  application. 

THE  ARCHITECT'S  LEVEL. 


Price  as  shown,  with  tripod,  $50.00. 

This  figure  represents  the  level  introduced  by  us  in  1874,  and 
which  has  since  been  very  largely  used  by  architects,  builders,  en- 
gineer?, and  surveyors,  in  the  grading  of  streets,  drives,  sewers,  etc., 
in  all  parts  of  the  country. 

It  has  a  telescope  12  inches  long,  furnished  with  rings,  wyes,  ere, 
precisely  like  our  larger  levels,  and  adjusts  in  the  same  way. 

The  leveling  head  has  the  ordinary  screws  and  a  clamp  to  the 
spindle;  it  has  also  a  horizontal  circle  3  inches  in  diameter,  fitted  to 
the  upper  end  of  the  socket,  and  turning  readily  upon  it;  the  circle 
is  graduated  to  degrees,  figured  from  o  to  90  each  way,  and  is  easily 
read  to  five  minutes  of  a  degree  by  a  vernier  which  is  fixed  to  the 
spindle. 

The  adjustments  are  not  liable  to  derangement,  and  ordinarily  re- 
quire but  little  attention. 

A 


221 


TROY,  N.  Y. 

FARMER'S  OR  DRAINAGE  LEVEL. 


Price,  as  shown,  with  tripod,  $25.00. 

This  Level  combines  the  extremes  of  simplicity  and  compactness 
with  real  efficiency,  and  at  moderate  cost.  The  telescope,  9  inches 
long,  is  achromatic,  and  of  sufficient  power.  The  cross  wires  are 
not  easily  disturbed.  The  level  and  telescope  are  both  inclosed  in 
an  outer  bronze  case.  The  instrument  is  approximately  leveled  by 
the  ball  spindle  on  the  socket  and  then  precisely  so  by  the  leveling 
screws.  The  advantage  of  this  form  of  Level  in  the  work  of  the 
farmer  in  laying  out  ditches  and  reservoirs  will  be  apparent  on  in- 
spection. When  desired  we  add  to  this  level  a  3-inch  needle  mag- 
netic compass  at  an  extra  cost  of  $5.  This  is  fitted  to  the  case  as 
shown  below  and  can  be  removed  at  pleasure. 


222 


223 


WELL  MACHINERY. 


gend   for  our  (Catalogue 

DESCRIBING  A  FULL  LINE  OF 

ARTESIAN  WELL  OUTFITS, 
PORTABLE  ROCK  DRILLS, 

AND  THE   CELEBRATED 

Petzh  Well  /lugeF, 

WIND  MILLS, 

GENERAL  WELL  SUPPLIES, 

&c..  &c. 


THE  PECH  MFE.  CO., 

SIOUX  CITY,  IOWA. 


224 


Valve  Manufacturing  Co., 


MANUFACTURERS  OF 


Valves  ai?d  F!FE 


Double  and  Single  Gate 

VALVES, 

ALSO 

Check  Valves, 
Foot  Valves, 

and  Vard  and  Wash 

HYDRANTS- 


FACTORY  AND  OFFICE. 

938  to  954  River  St., and  67  to  83  VaiJ  Ave., 

TROY,  N.  Y.,U.  S.A. 

IFOIR, 


225 

WELL  DRILLING 
[  MACHINERY, 

AND  TOOLS,   ADAPTED    TO    ALL    KINDS 

of  work,  and  prospecting. 

Horse  and  Steam  Power. 
They  never  fail.    They  are  Sim- 
ple, Practical,  and  Thorough. 

We  also  make 
a  full  line  of  gas  and 

Water  Works  Goods, 
Gate  Valves,  &  Hydrants. 

Our  open-way  hydrants  are  the 
best  in  the  market. 

Corporation     Cocks, 

and  the  best 

Tapping  Machine 

in  the  world. 


Write  for  Circalars,  and  let  us  talk 
it  over  with  you. 

Address  the 

Brass  X  Iron  Works  Go, 

FOSTORFA,  OHIO. 


226 

THE  PELTON  WATER  WHEEL. 

Affords  the  most  efficient  and  reliable  power  for  all  purposes,  be- 
ing especially  adapted  to  utilize  the  power  from  ARTESIAN 
WELLS.  They  are  warranted  to  give  from  25  to  40  per  cent  better 
results  than  any  other  wheel.  The  Woonsocket  and  Yankton  Mills 
and  Huron  Electric  Lights  are  run  with  Pelton  wheels. 
(See  page  81.) 

PELTON  WATER  MOTORS, 

embrace  the  smaller  wheels  set  in  iron  casings  ready  for  pipe  connections 
Made  of  capacities  from  a  fraction  of  1,  up  to  50  horse  power.  The  cheap 
est  and,  most  convenient  power.  Parties  interested  in  the  development  of 
Dakotas  great  artesian  power  will  be  furnished  with  catalouge,  circulars, 
and  other  information  on  demand  to  the 


227 


Oil  Well  Supply  Co., 

PITTSBURGH,  PENN. 

Manufacture  every  article,  tool  or  appliance 
needed  at 

ARTESIAN  WELLS. 


ARTESIAN 

WELL 
MACHINERY. 


Boilers,  Engines,  Pxnrxps, 
Derricks,  Cordage,  "Filings, 
Drilling  and  Yislving  Tools, 
Txitoing    and    Casing. 

and  Iron  Good?  and  Supplier 


For  Steam,  Gas,  Petroleum  or  Water.     Catalogues  and  Price  Lists 
on  application. 


228 
W.   E.  SWAN.  P.   J.  STAGEY. 

W.  E.  SWAN  CO., 

ANDOVER,  S-  D. 


Drilled  the  first  well  in  Dakota,  at  Aberdeen. 


Have  had  TEN  YEARS'  experience  IN  DAKOTA. 

Being  the  oldest  drillers  in  the  state,  and 
having  the  most  experience  in  the  hard  Dako- 
ta formations,  and  the  best  rigs  and  most  im- 
portant tools  we  are  better  equipped  for  rapid 
and  successful  work  than  any  drillers  in  the 
Dakota  basin.  Our  experience  extends  over  6 
states  and  our  record  is  as  good  as  our  experi- 
ence is  broad  and  varied.  We  are  prepared  to 
drill  to  any  depth  and  of  any  size.  Among  our 
wells  are  the  following: 

WELLS   IN    N.   AND  S.    DAKOTA. 

Aberdeen, 
Columbia, 

Groton  "  WOTS  in  Manitoba, 

\ndover  Many  in  Minnesota. 
Ashton,  '  Wisconsin. 

Huron  Iowa- 

Mellette,  Illinois. 

Devils  Lake, 
Bismarck, 

Grafton,  Correspondence  solicit- 

Frankiort,  ed.     (»ive  us  a  chance 

Ipswich,  to  bid  on  your  work  if 

And    many  farm  wells  you    want    good  work 

in  both  states.         and  promptly  done. 


230 

The  Great  Northwest 

is  traversed  by  the 

Chicago   &  Northwestern 
Railway. 

The  finest  cars  in  the  land  are  run  on  its 
trains  between  Chicago  and  all  the  principal 
points  in 

ILLINOIS,         HRfQRffl  NEBRASKA, 
WISCONSIN,    IE9lfH|j|  SOUTH  DAK., 
MINNESOTA,    !ffifffl  H   AND  IOWA. 


Chicago, 

Milwaukee, 

Madison, 

St.  Paul, 

Minneapolis, 

Duluth, 

Ashland, 

Superior, 

Winona, 

Council  Bluffs, 

Omaha, 

Des  Moines, 

Sioux  City, 

Sioux  Falls, 

Mitchell, 

Huron, 

Watertown, 

Pierre, 

Aberdeen, 

and 

Oakes, 

are  all  reached  by  our  lines. 

Parties  desiring  to  visit  the  great 

ARTESIAN  BASIN 

of  Dakota  should  take  this  line  for  all  the  great  artesian 
wells  are  reached  by  our  road. 


The  best  farming  land  in  America  is  to  be  had  in 
the  Dakotas  where  IRRIGATION  BY  ARTE- 
SIAN WELLS  will  make  every  farmer  rich. 


231 


Profitable  Investments. 


THE  CHICAGO  AND 

No  RTH  •  WESTERN 

RAILWAY  CO. 

Owns  Lots  in  most  of  the  Cities  and  Towns  on  its}lines  in 

SOUTH  DAKOTA. 


These  Lots  are  For  Sale 

at  such  prices  and  terms  as  to  secure  to  purchasersjsafe  and 
profitable  investments. 


South  Dakota  is  All  Right, 

and  those  seeking  locations  for  investments,  or  opportunities 

for  the  investment  of  capital,  should  give  it  an 

intelligent  investigation. 


For  particulars  apply  to 

CHAS,  E,  SIMMONS, 

Land  Commissioner  C*  &  N.-W.  Ry.  Company, 
CHICAGO,    ILLINOIS. 


232 


A  GREAT  RAILWAY. 

The  CHICAGO,  MILWAUKEE  &  ST,  PAUL  RAIL- 
WAY COMPANY  now  operates  over  sixty-one  hun- 
dred miles  of  thoroughly  equipped  road  in  ILLINOIS, 
WISCONSIN,  NORTHERN  MICHIGAN,  MINNESOTA, 
IOWA,  MISSOURI,  SOUTH  and  NORTH  DAKOTA. 
Each  recurring  year  its  lines  are  extended  in  all  di- 
rections to  meet  the  necessities  of  the  rapidly  popu- 
lating sections  of  country  west,  northwest  and 
southwest  of  Chicago,  and  to  furnish  a  market  for 
the  products  of  the  greatest  agricultural  and  stock 
raising  districts  of  the  world.  In  Illinois  it  operates 
317  miles  of  track;  in  Wisconsin  1,636  miles;  in 
Northern  Michigan  96  miles;  in  Iowa  1,551  miles: 
in  Minnesota  1,115  miles;  in  South  Dakota  1,092; 
in  North  Dakota  118  miles;  in  Missouri  140  miles, 
and  the  end  is  not  yet.  It  has  terminals  in  such 
large  cities  as  CHICAGO,  MILWAUKEE,  LA  CROSSE, 
ST.  PAUL,  MINNEAPOLIS,  FARGO,  Soiux  CITY, 
COUNCIL  BLUFFS,  OMAHA  and  KANSAS  CITY  and 
ST.  JOSEPH,  MISSOURI,  and  along  its  lines  are  hun- 
dreds of  large  and  small  thriving  cities,  towns  and 
villages.  Manufacturing  interests  are  cultivated, 
and  all  branches  of  trade  find  encouragement.  The 
Railway  Company  has  a  just  appreciation  of  the 
value  of  its  patrons,  and  its  magnificent  earnings 
are  the  result  of  the  good  business  tact  which  char- 
acterizes the  management  of  its  affairs. 


233 

THE  POPULARITY  OF  THE 

Chicago,  Milwaukee  and  St.  Paul 
Railway 

is  attested  by  the  fact  that  notwithstand- 
ing the  strongest  kind  of  competition  of 
old  and  new  lines,  the  Chicago,  Milwaukee 
&  St  Paul  Railway  continues  to  carry  the 
greater  proportion  of  all  the  business  be- 
tween Chicago,  Milwaukee,  St.  Paul  and 
Minneapolis.  It  is  the  best  patronized 
route  between  Chicago,  Council  Bluffs 
and  Omaha  and  to  and  from  all  points  in 
Wisconsin,  Minnesota,  Dakota  and  Iowa, 
and  its  Kansas  City  and  St.  Joseph  line 
has  taken  equal  rank  with  the  older  lines 
leading  to  and  from  the  Southwest. 

On  all  its  THROUGH  LINES  of  travel  the 
CHICAGO,  MILWAUKEE  &  ST.  PAUL  RAIL- 
WAY runs  the  most  perfectly  equipped 
trains  of  Sleeping,  Parlor  and  Dining 
Cars.  The  through  crains  on  all  its  lines 
are  systematically  HEATED  BY  STEAM. 
No  effort  is  spared  to  furnish  the  best  ac- 
commodations for  the  least  money,  and,  in 
addition,  patrons  of  the  road  are  sure  of 
courteous  treatment  from  its  employes. 


234 
THE 

Engineering  Magazine 

A  high-class,  beautifully  illustrated  monthly  magazine, 
like  the  Century  and  Harper's,  but  devoted  exclusively  to 
industrial  affairs  and  engineering  problems.  It  covers  the 
entire  field  of  industry,  and  besides  nine  special  depart- 
ments, and  a  monthly  index  to  all  that  is  of  value  in  tech- 
nical literature,  each  number  contains  ten  leading  articles 
by  distinguished  authorities  upon  topics  that  are  uppermost 
in  public  interest. 

The  following  are  among  the  leading  articles  published  in 
recent  numbers: 

Progress  in  Aerial  Navigation,  (Illustrated) 

O.  Chanute,  president  American  Society  C.  E. 

The  Future  of  our  Wagon  Koads— Wm.  Claypoole,  C.  E. 

The  Solution  of  the  Block  Signal  Problem,  (111.) 

H.  Ward  Leonard,  E.  E. 

Is  the  limit  reached  in  armored  Warships? 

Albert  Williams,  Jr.,  E.  M. 

Pure  Water  and  Public  Health. 
Floyd  Davis,  Ph.  D.  Chemist,  Iowa  State  Board  of  Health. 

The  Canadian  Pacific  Bailroad— T.  K.  Thomson,  C.  E. 

Worthless  Government  Engineering— Geo.  Y.  Wisner,C.  E. 

Followed  by  a  criticism  by  Lieut.  Col.  W.  B.  King  of  the 
Engineer  Corps,  and  a  rejoinder  by  the  author. 

The  World's  Store  of  Tin,  (111.)  E.  W.  Claypole,  A.  B.,  D.  Sc. 

The  Bights  of  the  Lowest  Bidder;  What  the  Contractor 
Wants  to  Know,  L.  Allen,  A.  B.,  M.  E. 

The  Answer  of  the  Law,  C.  E.  Hellier,  LL.  B. 

The  Decline  in  Bailroad  Building,  T.  L.  Greene. 

The  Wind  as  a  factor  in  Geology  (111.),  G.  P.  Merrill. 

The  Manufacture  of  Ice,  L.  Allen,  A.  B.,  M.  E. 

The  Purification  of  Water,  F.  Davis,  Ph.  D. 


'Edited  with  marked  ability."— Boston  Herald. 

'Readable  from  cover  to  cover."— Indianapolis  News. 

'Studded  with  ideas  of  practical  value."—  Norfolk  Virginian. 

The  contributors  are  men  of  the  highest  rank."— St.  Louis  Eepublic. 

'We  heartily  commend  it  to  the  general  public."— Post  on  Transcript. 

'Unquestionably  the  most  elaborately  illustrated  engineering  journal 
that  has  yet  appeared  on  either  side  of  the  Atlantic. "—Mechanical  World 
London. 

PRICE— 25  cents  a  number;  $3.00  a  year.  At  all  news 
stands,  or  by  mail.  Send  10  cts.  for  a  sample  copy,  and  men- 
tion this  manual. 

THE  ENGINEERING  MAGAZINE  CO., 

World  Building,  NEW  YORK,  U.  S.  A. 


235 


Great  Northern   Ry, 

Has  3  lines  in  South  Dakota,  connecting 

Sioux  Falls,  Huron,  Watertown  and  Aberdeen 

WITH 

St,  Paul, 
Minneapolis, 
Mutt, 
Superior 


AND  THE 

EAST. 

Reaches  more 
points  in 

Minnesota, 


AND 


North  Dakota 

than  any  other 
line. 


Has  2  Lines 

from  St.  Paul  and 

Minneapolis 

to  the 


It  is  the  direct  route  to  GREAT  FALLS,  HELENA  and 
BUTTE.  Gives  choice  of  TWO  ROUTES  TO  THE  PA- 
CIFIC COAST.  Round  Trip  Tourist  Tickets  to  all  the 
leading  points  in  the  west.  For  Maps,  publications  and  in- 
formation apply  to  any  agent  of  the  Co.,  or  address 

F.  I.  WHITNEY,  G.  P.  &  T.  A., 

ST.  PAUL,   MINN. 


236 


*    TAKE   THE    * 

Northern 
Pacific 

Railroad. 

— 

A  -H*  Car  Lin. 


TO    ALL    PRI  NCI  PALI  POINTS    IN 


The  Greatjorthwest 

For  Rates,  Time-Tables  and  Illustrated 
Tourists'  Publications,  address 

J.  N.  HANNAFORD,  CHAS.  S.  FEE,  " 

^Gen'l  Traffic  Manager,  ^j      :j      Gen'l  Pass.  &  Ticket  Agent. 

St. 


Northern  Pacific 
Railroad, 


237 


•j 


[IMPROVED.! 

in  the   \V)orld. 

Specially  adapted  to  high  pressure 

service  for  running  machinery  of  all 

kinds,  from  %  to  15  horse-power. 


Manufacturer.-;  of 

Little    Giant    Water    Motors 

The  B.    C.    Standard    Electric 

Motors  and  Dynamos,  the  Combined  Water  Motor 

and    Dynamo,    Combined    Engines   and    Dynamos, 

Water  Motor  Cyclone  Coffee  Mills,  and  Electric  Motor  Church 
Organ  Piston  Motors.     Also  all  other  Electrical  Supplies. 


238 


ROOT'S 

Steel  or  Iron  Spiral  Riveted  Pipe 

3  to  24  inches  diameter.     2  to  25  feet  lengths. 

Connections  and  Fittings  to  suit  service 

required.     Unrivaled  for 

Water  Works,  Hydraulic  Mining 

AND 

IRRIGATION, 


AS  HAS  BEEN  PROVED  BY 


14  2Jeap$  Practical 

(See  pages  24,  122,  123  herein.) 


Facfory  at 

Greenpoint,  L.  I. 


New  York  Office 

28  Cliff  Street. 


Pacific  Coast  Office,  23   Davis  Street, 
San   Francisco,  Cat. 

A.  L.  ALDERSON,  Representing  GEO.  F.  EBERHARD,  Mgr. 


ABENDROTH  &  ROOT  MFG.  CO. 

(See  next  page  also.) 


239 


(See  page  238.) 


o, 

•  i— H 

OH 

U 

OJ 

"o3 


CU 

-t— > 

CJ 


Abendroth  &  Root 
S.  Co.: 


Bolted  Joint  Section. 


240 


YOUNG  4  SONS, 


Manufacturers  of 


Engineering,  Mining,  and  Sur- 
veying Instruments. 


Established  1820. 


No.  43  North  Seventh  St.,  Philadelphia. 


241 


DRAINAGE  LEVELS. 


5ei?d  IOF  our  Special  Ligt  oT 

e  Bevels. 


Mailed  to  any  address  upon  application 


TO 


YOUNG  &  SONS, 


NO.  43  NORTH  7TH  ST.,  PHILADELPHIA. 


242 


FJobinson  §  Gang  Co., 


JOBBERS  OF 


Wrought 
Iron 


PIPE 


Cast 


Iron 


FITTINGS, 

PUMPS,  VALVES, 

x&C, 
ENGINES,  BOILERS, 

MACHINERY, 


Railway,  Miners' &  Mill  Supplies 


4TH  *  WACOUTA  STS., 


St.  Paul,     -     Minnesota. 


243 


SWAN  BROS., 
Well  Drillers, 

ANDOVER,  SOUTH  DAKOTA. 


"BY  THEIR  DEEDS  SHALL  YE  KNOW  THEM." 


QQ 


OQ 


We  have  drilled  wells  in  all  parts  of  the  Dakotas,  in  Wis- 
consin, Iowa,  Minnesota  and  in  the  Canadian  Northwest. 
We  are  always  successful.  We  use  the  best  rigs,  tools,  and 
machinery,  and  we  are  acknowledged  to  be  the  best  drillers 
in  this  field.  We  let  our  work  speak  for  us. 
Correspondence  solicted. 


244 


Time  Tested,  Best  and  Cheapest  Automatic  Steam  Vacuum  Pump  Known, 
for  Irrigation,  Mining  and  General  Farm  Purposes, 


Requires  no 
Engine,  Belt- 
ing, Housing, 
Oil,  Packing, 
Attention  or 
Expensive 


Over  21,i 
in  use 


f 

Has  no 
Piston  Rods , 
Cranks,  Eccen- 
trics, Levers, 
Beams,  Jets, 
Weights  or 
other  Compli- 
cated Mechan- 
ism to  get  out 
of  order  and 
absorb  power, 

* 


Requires  Less  Steam  and  Fuel  than  other  Pumps. 
OPERATES  HUNG   UP  OR  STATIONERY. 

ANYBODY  CAN  OPERATE  IT 

IT  WILL  NEVER  WEAR  OUT, 

Catalogues,  Estimates  and  Particulars  Furnished  on  Application 
TO 

THE  PULSOMETER  STEAM  PUMP  CO., 

Sole  Owner  and  Manufacturer, 

NEW  YORK. 
See  also  pages  126, 127,  128  . 


245 


ARTESIAN  IRRIGATION  IN  ITS  PERFECTION. 
Where  power  of  well  is  used  for  Threshing  and  Grinding  Feed. 


\  .    We  B\xy  ,  Irrigate,  and  Sell  l_iand-. 

2.  We    Sink.     Rrtesian   Wells   \>y 

Contract. 

3.  "We  Bent  l_iai\d  and  Pay  Taxes 

lor  ^cm-resi&en^s    and  Corpo- 
raUons. 


4.    We  Sell   \tae   Best   Paying  and 
Salest  Seoxxrities  in  tlie  \3  .  S. 


Dakota  Irrigation 

ABERDEEN,  S.  D. 

S.  W,  Narregang,  President,  Excelsior  Block- 


246 

The  Western  Wheeled  Scraper  Co,, 

AURORA,  ILL. 

(Formerly  oi  Mount  Pleasant,  Iowa.) 

THE    LEADING    MANUFACTURERS    OF 
GRADING  IMPLEMENTS. 

Our  celebrated 

Western  Wheeled 
SCRAPERS 

are  used  in  all  parts  of 
the  world.  Our 

Western  Double- 
bottom  Drag 
SCRAPERS 

are  un equaled  and  are 
the  favorite  with  all 
graders. 

We  make  the  MOORE  IRRIGATING  DITCHER  which  is 
extensively  used  in  all  the  Western  States  for  making  Irri- 
gating Ditches  and  laterals,  and  for  leveling  land.  We  also 
make  the 

I^est  Road  TVlacbine  on  garth. 

Also  Wheelbarrows,  Dump-Carts  and  Farm  Wagons. 

Send  for  Catalogues  and  Prices  to  the 

)beeled  §craj>er  G°.> 

AURORA,  ILLS. 


247 


IsTSTIE'S 

STEAM  VACUUM    PUMPS 


FOR 


IRRIGATION,  Etc. 


TYie  Cheapest, 

TY\e  Simplest, 

and.  \,tie  most, 
Pump  m 


The  pump  works  equally  well  if  the  water  is  loaded  with 
sand  or  gravel  . 


Ho  Pistons,  no  parts  to  Wear  or  Break. 

Any  man  or  boy  can  manage  it. 
(See  page  126.) 


Please  write  for  Catalogue  and  full  information,  to  the 
NYE  STEAM  VACUUM  PUMP  CO., 

7  and  9  S.  Jeffers  >n  St.,  Chicago,  111. 


248 


500FOOT 

MACHINE 

set  up  in  30 

MINUTES. 


ANY  ONE 

can 
RUN  IT. 


later  Your  Farms  and  Irrigate  Your  Lands 

WITH  THE  VERY  BEST  AND  CHEAPEST 

Artesian  W)ell 

For  wells  2.000  feet  or  less  ten  sizes  set  up  and  has  the 
well  half  way  down  before  an  ordinary  ^Derrick"  couid  be 
built.  Drills  30  to  80  feet  per  24  hours  in  hard  rock.  Manu- 
factured in  the  great  oil  fields  of  Pennsylvania.  Ko  extras 
needed  with  these  machines.  Made  with  or  without  "trac- 
tion attachment."  Our  2,000  foot  rig  can  be  run  by  a 
thresher  engine.  Buy  one  and  make  money  with  your  idle 
thresher  engine  the  year  round.  A  skilled  operator  sent 
free  to  set  and  start  each  machine  and  give  full  instructions 
in  its  use.  Every  machine  guaranteed. 

Correspondence  solicited  from  parties  wanting  artesian  wells. 

SOLD  DIRECT  TO  USERS  AT 

MANUFACTURERS  PRICES. 

Catalogue  of  Artesian  Irrigating 

IPTJIMIIIPS 

for  wind  or  steam  pow- 
er. Can  be  run  with  a 
thresher  engine.  Will 
save  50  per  cent,  of 
power,  and  do  more 
work  than  any  other 
pump. 

KEYSTONE 

DRILLER  CO., 

Beaver  Falls,  Penn. 


249 

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250 

JOHN   H.   MILLER.   PRES.  JOHN   L.  PYLE,  SEC. 

W.    N.   COLER,   VICE   PRES.  ALVA  E.  TAYLOR,   TREAS 


Valley  Land  and  Irrigation  Company, 


HURON,  SOUTH  DAKOTA. 


CAPITAL  STOCK,  $2,000,000.     INCORPORATED  1891. 


100,000  ACRES  OF  FARM  LANDS  IN 
THE  ARTESIAN  BELT 

FOR  SALE  ON  EASY  TERMS. 


Address: 

NORTH  AMERICAN  LOAN  &  TRUST  CO.,  Agents, 

190  and  192,  Dearborn  St.,  Chicago,  111. 


First  National  Bank 

UNITED  STATES  DEPOSITORY, 

HURON. SOUTH   DAKOTA. 

,  $7^,000.    garplus,  $1^,000. 


R  (SerjEFal  Banking  BugirjEss 


THOS.    H.   CAMPBELL,   President. 
J.   W.  MACKENZIE,   Cashier. 
ED.  J.   MILLER,   Assistant  Cashier. 


251 


ARTESIAN  IRRIGATION 

CONSOLIDATED 
LAND  AND  *  IRRIGATION 

COMPANY, 

HURON,    SOUTH    DAKOTA. 


(,  Reliable  7Wedium  for 
both  J-Juj/ercind 
Seller  of  goutb 


JOHN  E.  DIAMOND,  PRESIDENT. 

D.   L.    BUSH,  VICE-PRESIDENT. 

M.  H.  PRICHARD,  SEC.  &  TREAS. 

R.    O.    RICHARDS,     MANAGER. 


Irrigated,  Sought,  Sold 
and  Managed. 


251  A 


See  Advertisements 

OF 

Wra 
•    X* 

ON 

pages  2  and  41. 


251  B 

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LIBRARY 


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FEB 


7    M 


(Or   II    an< 


H  book  was  charged  out. 

AIT  orks, 


lias,    Texas;    and 


WAT] 
PR 

Operated  b 
Interested  .f| 

Elip 

Combi] 

ST 

Deep 
P 


IS,    AND 
TERY, 

•fijy  SIZE  HOLE, 
corn- 

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UNIVERSITY  OF  CALIFORN 
1  778          BERKELEY,  CA  94> 


J 


YA  01453 


HADING  IRON  CO, 


Manufacturers  of 


BROUGHT  IRON  PIPE 

DRIVE  PIPE, 

tesian  or  Oil  Well  Tubinsj  an^'Jasing, 
BOILER 


Basing, 

taper-tapped 


(See  above  cut.) 


or  Deep  Artesian  Wells. 


Chicago  Office, 
22  W.  Randolph  Street, 
.  SAMUEL  CLIFFORD,  Agtj 


.     Communicate 
wlth  us  and  Get  Prlces- 


See  pages  16,  17,  19,  25. 


